Skip to main contentModule prelude
Source pub use crate::work;pub use crate::force;pub use crate::torque;pub use crate::momentum;pub use crate::pressure;
- AngularState
- A scalar angular position and angular velocity pair.
- CantileverReaction
- Fixed-end reaction data for a cantilever with a free-end point load.
- CentralBody
- Mass and optional radius for a central body used in orbital calculations.
- Collision1D
- A one-dimensional collision configuration with two bodies and a restitution coefficient.
- CollisionBody1D
- A one-dimensional body with scalar mass and velocity.
- ConstantForceWork
- Constant-force work inputs for repeated calculations.
- DecayLaw
- Simple exponential-decay law parameterized by a decay constant.
- Dose
- A simple absorbed dose wrapper in gray.
- ElasticBar
- Simple uniform elastic bar properties for axial loading summaries.
- ElasticMaterial
- Simple elastic material parameters for linear isotropic summaries.
- ElectricalLoad
- A simple electrical load described by voltage and resistance.
- ElectromagneticField
- A scalar electric and magnetic field pair.
- ElectronPlasma
- A simple electron-plasma state.
- ElementaryCharge
- An exact electric charge expressed in thirds of the elementary charge.
- EllipticalOrbit
- Elliptical orbit state described by a gravitational parameter and apsides.
- Fluid
- A simple fluid model with density and optional dynamic viscosity.
- Force2D
- A validated planar force value.
- GravityBody
- Mass and radius for a body used in gravity calculations.
- LeverForce
- A force applied at a lever arm.
- MagneticField
- A simple magnetic field described by flux density.
- MassProperties
- Mass and rotational inertia for a scalar rigid body.
- MatterWave
- A lightweight matter-wave wrapper stored by momentum magnitude.
- MovingMass
- A moving mass with scalar velocity.
- NuclideNumbers
- Mass and atomic numbers for a nuclide.
- Particle
- A lightweight particle wrapper that delegates to the free helper functions.
- Photon
- A lightweight photon wrapper stored by energy in joules.
- PipeFlow
- A simple cross-sectional pipe flow with area and scalar velocity.
- PlasmaSpecies
- A simple scalar plasma species description.
- PointForce2D
- A planar force applied at a position relative to a chosen moment point.
- QuantumNumbers
- Quantum numbers for a single-electron atomic-state style validation helper.
- RadiationBeam
- A simple beam characterized by total power and illuminated area.
- RelativisticBody
- A body with scalar rest mass and signed velocity.
- RigidBody1D
- A one-dimensional rigid body with scalar translational and rotational state.
- RotatingBody
- A rotating body with scalar moment of inertia and angular velocity.
- Shield
- A simple slab shield with a linear attenuation coefficient and thickness.
- SimpleHarmonicOscillator
- A simple scalar harmonic oscillator state.
- Spin
- A spin value expressed as doubled units of
hbar. - SpringOscillator
- A spring-mass oscillator state.
- StaticSystem2D
- A simple planar static system made of force vectors and scalar moments.
- TorqueSystem
- A collection of torque values that can be analyzed as a system.
- DensityError
- MotionError
- ParticleFamily
- Broad family groupings for the supported particles.
- ParticleKind
- Identifies a supported particle kind.
- ParticleStatistics
- Spin-statistics classification for the supported particles.
- PowerError
- PressureError
- RadiationKind
- Simple radiation categories for scalar helper selection.
- ThermodynamicsError
- ATOMIC_MASS_UNIT_MEV_C2
- Atomic mass unit energy equivalent in mega-electron-volts per
c^2. - BOHR_RADIUS
- Bohr radius
a0, in meters. - BOLTZMANN_CONSTANT
- Boltzmann constant in joules per kelvin.
- COULOMB_CONSTANT
- Coulomb’s constant for electrostatic force calculations.
- ELECTROMAGNETISM_SPEED_OF_LIGHT
- Speed of light in vacuum, in meters per second.
- ELECTROMAGNETISM_VACUUM_PERMEABILITY
- Vacuum permeability in henries per meter.
- ELECTRON_MASS
- Electron rest mass, in kilograms.
- ELEMENTARY_CHARGE
- Elementary charge, in coulombs.
- GRAVITATIONAL_CONSTANT
- Newtonian constant of gravitation, in cubic meters per kilogram second squared.
- IDEAL_GAS_CONSTANT
- JOULES_PER_MEV
- Joules in one mega-electron-volt.
- LN_2
- Natural logarithm of
2 for half-life conversions and decay-law helpers. - PLANCK_CONSTANT
- Planck constant
h, in joule seconds. - PLASMA_ELECTRON_MASS
- Electron mass in kilograms.
- PLASMA_ELEMENTARY_CHARGE
- Elementary charge in coulombs.
- PLASMA_VACUUM_PERMEABILITY
- Vacuum permeability in henries per meter.
- PLASMA_VACUUM_PERMITTIVITY
- Vacuum permittivity in farads per meter.
- PROTON_MASS
- Proton mass in kilograms.
- QUANTUM_SPEED_OF_LIGHT
- Speed of light in vacuum, in meters per second.
- RADIATION_JOULES_PER_MEV
- Joules in one mega-electron-volt.
- RADIATION_SPEED_OF_LIGHT
- Speed of light in vacuum, in meters per second.
- REDUCED_PLANCK_CONSTANT
- Reduced Planck constant
hbar, in joule seconds. - RELATIVITY_SPEED_OF_LIGHT
- Speed of light in vacuum, in meters per second.
- RYDBERG_ENERGY_EV
- Hydrogen Rydberg energy magnitude, in electron volts.
- SPEED_OF_LIGHT
- Speed of light in vacuum in meters per second.
- STANDARD_GRAVITY
- VACUUM_PERMEABILITY
- Vacuum permeability in newtons per ampere squared.
- VACUUM_PERMITTIVITY
- Vacuum permittivity in farads per meter.
- absolute_pressure
- Computes absolute pressure from surface pressure and the hydrostatic contribution.
- absorbed_dose
- Computes absorbed dose with
D = E / m. - absorbed_energy_from_dose
- Computes absorbed energy from dose with
E = D * m. - acceleration
- Computes acceleration for simple harmonic motion using
a(t) = -Aω² * cos(ωt + φ). - acceleration_from_displacement
- Computes simple-harmonic acceleration from displacement using
a = -ω²x. - accumulated_dose
- Computes accumulated dose with
D = dose_rate * t. - activity
- Computes activity from a decay constant and number of nuclei.
- alfven_speed
- Computes the Alfven speed.
- altitude_from_orbital_radius
- Computes altitude from body radius and orbital radius.
- angular_acceleration
- Computes angular acceleration using
α = (ω_final - ω_initial) / t. - angular_acceleration_from_torque
- Computes angular acceleration from torque and moment of inertia.
- angular_displacement
- Computes angular displacement using
θ = ω_initial * t + 0.5 * α * t². - angular_frequency_from_energy
- Computes angular frequency from energy using
omega = E / hbar. - angular_frequency_from_frequency
- Computes angular frequency from frequency using
ω = 2πf. - angular_frequency_from_period
- Computes angular frequency from period using
ω = 2π / T. - angular_impulse_from_angular_velocity_change
- Computes angular impulse from an angular velocity change using
J = I(ω_final - ω_initial). - angular_momentum
- Computes angular momentum using
L = Iω. - angular_velocity
- Computes angular velocity using
ω = Δθ / t. - angular_velocity_after_angular_impulse
- Computes final angular velocity after an angular impulse using
ω_final = ω_initial + J / I. - angular_velocity_from_angular_momentum
- Computes angular velocity from angular momentum using
ω = L / I. - angular_velocity_from_rotational_kinetic_energy
- Computes angular velocity from rotational kinetic energy using
ω = sqrt(2KE / I). - angular_velocity_from_tangential_speed
- Computes angular velocity from tangential speed using
ω = v / r. - antiparticle
- Returns the modeled antiparticle for
kind. - apoapsis_from_semi_major_axis_eccentricity
- Computes apoapsis radius from semi-major axis and eccentricity.
- apoapsis_speed
- Computes speed at apoapsis using the vis-viva equation.
- attenuated_intensity
- Computes attenuated intensity with
I = I0 * e^(-mu * x). - average_force_from_impulse
- Computes average force from impulse and elapsed time using
F = J / Δt. - average_power
- Computes average power from total work and elapsed duration.
- average_speed
- Computes average speed from traveled distance and elapsed duration.
- axial_deformation
- Computes axial deformation of a prismatic bar under linear elastic loading.
- axial_stiffness
- Computes axial stiffness of a uniform elastic bar.
- balancing_force
- Computes the balancing force needed at a lever arm to cancel a known torque.
- balancing_lever_arm
- Computes the balancing lever arm needed for a force to cancel a known torque.
- bernoulli_pressure
- Computes downstream pressure from the Bernoulli relation between two points.
- beta
- Computes the dimensionless speed ratio
β = v / c. - beta_from_rapidity
- Computes
β = tanh(φ) from rapidity. - binding_energy_mev_from_mass_defect_u
- Computes binding energy in mega-electron-volts from a mass defect in atomic mass units.
- binding_energy_per_nucleon
- Computes binding energy per nucleon.
- bohr_orbit_radius
- Computes the hydrogen-like Bohr orbit radius for
Z = 1 using r_n = a0 * n^2. - bulk_modulus
- Computes bulk modulus from pressure change and volumetric strain.
- bulk_modulus_from_youngs_and_poisson
- Computes bulk modulus from Young’s modulus and Poisson’s ratio.
- buoyant_force
- Computes buoyant force from fluid density, displaced volume, and gravitational acceleration.
- can_static_friction_hold
- Checks whether static friction can hold a body at rest.
- cantilever_end_point_load_reaction
- Computes the fixed-end reaction for a cantilever with a downward load at the free end.
- celsius_to_kelvin
- center_moment_from_parallel_axis
- Computes the center moment from a shifted moment using
I_cm = I - md². - center_of_mass_1d
- Computes the one-dimensional center of mass using
x_cm = Σ(m_i * x_i) / Σm_i. - centripetal_acceleration_from_angular_velocity
- Computes centripetal acceleration using
a_c = ω²r. - centripetal_acceleration_from_tangential_speed
- Computes centripetal acceleration using
a_c = v² / r. - change_in_length
- Computes change in length from strain and original length.
- change_in_volume
- Computes change in volume from volumetric strain and original volume.
- charge
- Returns the exact charge for
kind. - charge_density
- Computes charge density.
- charge_from_current_time
- Computes electric charge from current and elapsed time.
- charge_in_elementary_units
- Returns the charge in elementary-charge units.
- charge_thirds
- Returns the exact charge in thirds of the elementary charge.
- circular_orbital_period
- Computes the orbital period for a circular orbit.
- circular_orbital_speed
- Computes the speed for a circular orbit at a radius around a body with gravitational parameter.
- circular_orbital_velocity
- Computes the circular orbital velocity around a source mass.
- coefficient_of_restitution
- Computes the coefficient of restitution from approach and separation speeds.
- collision_energy_loss_1d
- Computes the total kinetic energy lost in a one-dimensional collision.
- collision_energy_loss_fraction_1d
- Computes the fraction of kinetic energy lost in a one-dimensional collision.
- collision_final_velocities_1d
- Computes the final velocities of a one-dimensional collision from masses, initial velocities,
and a coefficient of restitution.
- collision_impulse_on_a
- Computes the collision impulse applied to body A.
- collision_impulse_on_b
- Computes the collision impulse applied to body B.
- collision_impulses_1d
- Computes the impulses on both bodies for a one-dimensional collision.
- collision_kinetic_energy
- Computes kinetic energy from mass and one-dimensional velocity.
- combined_mass
- Computes the sum of non-negative masses.
- conductance
- Computes conductance from resistance.
- continuity_area
- Computes downstream area from continuity for incompressible flow.
- continuity_velocity
- Computes downstream velocity from continuity for incompressible flow.
- contracted_length
- Computes contracted length
L = L0 / γ from proper length L0. - coulomb_force
- Computes electrostatic force using Coulomb’s law.
- critical_damping_coefficient
- Computes the critical damping coefficient using
c_critical = 2 * sqrt(mk). - current
- Computes current from voltage and resistance using Ohm’s law.
- current_from_charge_time
- Computes current from electric charge and elapsed time.
- cyclotron_angular_frequency
- Computes cyclotron angular frequency using
ω = |q|B / m. - cyclotron_frequency
- Computes cyclotron frequency in cycles per second using
f = |q|B / (2πm). - cyclotron_radius
- Computes cyclotron radius using
r = mv / (|q|B). - damped_angular_frequency
- Computes the damped angular frequency for an underdamped oscillator.
- damping_ratio
- Computes damping ratio using
ζ = c / (2 * sqrt(mk)). - damping_ratio_from_quality_factor
- Computes damping ratio from quality factor using
ζ = 1 / (2Q). - de_broglie_wavelength
- Computes de Broglie wavelength from momentum magnitude using
lambda = h / p. - de_broglie_wavelength_from_mass_velocity
- Computes de Broglie wavelength from mass and velocity using
lambda = h / (m * |v|). - debye_length
- Computes the Debye length.
- debye_number
- Computes the Debye number.
- debye_sphere_volume
- Computes the Debye sphere volume.
- decay_constant_from_half_life
- Computes a decay constant from a half-life.
- decayed_fraction_from_decay_constant
- Computes the decayed fraction from a decay constant and elapsed time.
- decayed_quantity_from_decay_constant
- Computes the decayed quantity from an initial quantity, decay constant, and elapsed time.
- default_radiation_weighting_factor
- Returns a simple conventional radiation weighting factor for the given kind.
- degrees_from_radians
- Converts radians to degrees.
- density_of
- Computes density from mass and occupied volume.
- dilated_time
- Computes dilated coordinate time
t = γτ from proper time τ. - displaced_volume_from_buoyant_force
- Computes displaced volume from buoyant force, fluid density, and gravitational acceleration.
- displacement
- displacement_from_work
- Computes the displacement implied by a work value and a constant force.
- distance
- doppler_factor_longitudinal_from_beta
- Computes the longitudinal relativistic Doppler factor
D = sqrt((1 + β) / (1 - β)). - dose_rate
- Computes dose rate with
dose_rate = D / t. - downslope_force_incline
- Computes the downslope component of weight on an incline.
- drag_force
- Computes drag force from density, velocity, drag coefficient, and area.
- dynamic_pressure
- Computes dynamic pressure from density and flow velocity.
- dynamic_viscosity
- Computes dynamic viscosity from kinematic viscosity and density.
- earth_weight
- eccentricity_from_apsides
- Computes eccentricity from periapsis and apoapsis radii.
- effective_dose
- Computes effective dose with
E = H * w_T. - elapsed_time_from_remaining_fraction
- Computes elapsed time from a remaining fraction and decay constant.
- elastic_collision_final_velocities_1d
- Computes the final velocities of a perfectly elastic one-dimensional collision.
- elastic_energy_density
- Computes elastic strain-energy density.
- elastic_energy_from_force_deformation
- Computes elastic energy from force and deformation for a linear loading path.
- elastic_energy_from_spring_constant
- Computes elastic energy stored in a linear spring from stiffness and deformation.
- electric_field_energy_density
- Computes electric field energy density using
u_E = 0.5 * ε0 * E². - electric_field_for_velocity_selector
- Computes electric field magnitude for a selector using
E = vB. - electric_field_from_magnetic_flux_density_in_vacuum
- Computes electric field magnitude in vacuum using
E = cB. - electric_force_on_charge
- Computes electric force using
F = qE. - electrical_power
- electromagnetic_energy_density
- Computes combined electromagnetic energy density.
- electron_gyrofrequency
- Computes the electron gyrofrequency using electron mass and charge magnitude.
- electron_gyroradius
- Computes the electron gyroradius using electron mass and charge magnitude.
- electron_plasma_angular_frequency
- Computes the electron plasma angular frequency.
- electron_plasma_frequency
- Computes the electron plasma frequency in hertz.
- electron_thermal_speed
- Computes the electron thermal speed.
- electron_volts_to_joules
- Converts electron volts to joules using
J = eV * e. - elliptical_orbital_period
- Computes the orbital period for an elliptical orbit.
- energy_fluence
- Computes energy fluence with
Psi = E / A. - energy_from_angular_frequency
- Computes energy from angular frequency using
E = hbar * omega. - energy_from_mass_defect_kg
- Computes energy in joules from a mass defect in kilograms.
- energy_from_power_time
- Computes electrical energy from power and elapsed time.
- energy_from_voltage_charge
- Computes electrical energy from voltage and charge.
- energy_momentum_relation
- Computes total energy from rest mass and momentum using
E = sqrt((pc)² + (mc²)²). - equivalent_dose
- Computes equivalent dose with
H = D * w_R. - escape_speed
- Computes escape speed from a distance around a body with gravitational parameter.
- escape_velocity
- Computes the escape velocity from a source mass at a distance.
- family
- Returns the broad particle family for
kind. - final_angular_velocity
- Computes final angular velocity using
ω_final = ω_initial + αt. - final_angular_velocity_from_displacement
- Computes final angular velocity using
ω_final = sqrt(ω_initial² + 2αθ). - final_angular_velocity_squared
- Computes squared final angular velocity using
ω_final² = ω_initial² + 2αθ. - final_kinetic_energy_from_work
- Computes final kinetic energy from an initial kinetic energy and applied work.
- final_length
- Computes final length after elastic axial strain.
- final_velocity
- fluence
- Computes fluence with
F = N / A. - fluence_rate
- Computes fluence rate with
fluence_rate = F / t. - fluid_hydrostatic_pressure
- Computes hydrostatic pressure from fluid density, gravitational acceleration, and depth.
- force
- force_angle_radians
- Computes the planar angle of a force vector in radians.
- force_from_axial_deformation
- Computes force from axial deformation of a uniform elastic bar.
- force_from_stress
- Computes force from stress and cross-sectional area.
- force_from_torque
- Computes the force required to produce a known torque at a lever arm.
- force_from_work
- Computes the force required to perform a given amount of work over a displacement.
- force_magnitude
- Computes the magnitude of a planar force vector.
- frequency_from_angular_frequency
- Computes frequency from angular frequency using
f = ω / 2π. - frequency_from_period
- Computes frequency from period using
f = 1 / T. - frequency_from_photon_energy
- Computes frequency from photon energy using
f = E / h. - gauge_pressure
- gravitational_acceleration
- Computes the gravitational acceleration caused by a source mass at a distance.
- gravitational_force
- Computes the gravitational attraction between two point masses.
- gravitational_parameter
- Computes the standard gravitational parameter from a source mass.
- gravitational_potential_energy
- Computes gravitational potential energy between two masses.
- gravity_weight
- Computes weight from mass and gravitational acceleration.
- gyro_angular_frequency
- Computes the gyro angular frequency.
- gyrofrequency
- Computes the gyrofrequency in hertz.
- gyroradius
- Computes the gyroradius.
- half_life_from_decay_constant
- Computes a half-life from a decay constant.
- half_value_layer
- Computes half-value layer with
HVL = ln(2) / mu. - has_rest_mass
- Returns whether
kind has nonzero rest mass when that metadata is modeled here. - heat_energy
- hohmann_delta_v_1
- Computes the first burn for a Hohmann transfer.
- hohmann_delta_v_2
- Computes the second burn for a Hohmann transfer.
- hohmann_total_delta_v
- Computes the total scalar delta-v magnitude for a Hohmann transfer.
- hohmann_transfer_semi_major_axis
- Computes the semi-major axis of a Hohmann transfer ellipse.
- hohmann_transfer_time
- Computes the transfer time for a Hohmann transfer.
- hollow_sphere_moment_of_inertia
- Computes hollow-sphere moment of inertia using
I = (2 / 3)mr². - hydrogen_energy_level_ev
- Computes the hydrogen energy level in electron volts using
E_n = -Ry / n^2. - hydrogen_transition_energy_ev
- Computes the absolute transition energy between two hydrogen energy levels in electron volts.
- hydrogen_transition_wavelength
- Computes the photon wavelength for a hydrogen transition in meters.
- hydrostatic_pressure
- ideal_gas_pressure
- Computes ideal gas pressure from amount of substance, temperature, and volume.
- impulse
- impulse_from_momentum_change
- Computes impulse from a change in momentum using
J = p_final - p_initial. - impulse_from_velocity_change
- Computes impulse from a velocity change using
J = m(v_final - v_initial). - initial_kinetic_energy_from_work
- Computes initial kinetic energy from a final kinetic energy and applied work.
- intensity
- Computes intensity from power and area with
I = P / A. - inverse_square_intensity
- Computes inverse-square intensity from a reference value.
- ion_plasma_angular_frequency
- Computes the ion plasma angular frequency.
- is_antiparticle
- Returns
true when kind is represented as an antiparticle variant. - is_baryon
- Returns
true when kind is a baryon. - is_boson
- Returns
true when kind is a boson. - is_common_poisson_ratio
- Returns
true when Poisson’s ratio is finite and between 0.0 and 0.5, inclusive. - is_critically_damped
- Returns
true when the damping ratio is within tolerance of critical damping. - is_fermion
- Returns
true when kind is a fermion. - is_ionizing
- Returns whether the listed radiation kind is ionizing in this simple crate.
- is_lepton
- Returns
true when kind is a lepton. - is_meson
- Returns
true when kind is a meson. - is_overdamped
- Returns
true when the damping ratio represents an overdamped system. - is_particle_radiation
- Returns whether the listed radiation kind is particle radiation.
- is_perfectly_elastic
- Returns whether a valid restitution coefficient is effectively perfectly elastic.
- is_perfectly_inelastic
- Returns whether a valid restitution coefficient is effectively perfectly inelastic.
- is_photon_radiation
- Returns whether the listed radiation kind is photon radiation.
- is_quark
- Returns
true when kind is a quark. - is_quasi_neutral
- Checks whether a plasma is quasi-neutral within a relative tolerance.
- is_rotational_equilibrium
- Checks whether a torque system is in rotational equilibrium.
- is_self_antiparticle
- Returns
true when kind is its own antiparticle. - is_static_equilibrium_2d
- Checks whether a planar static system satisfies both translational and rotational equilibrium.
- is_subluminal_speed
- Returns
true when speed is finite, non-negative, and strictly less than the speed of light. - is_translational_equilibrium_1d
- Checks whether a 1D force system is in translational equilibrium.
- is_translational_equilibrium_2d
- Checks whether a 2D force system is in translational equilibrium.
- is_underdamped
- Returns
true when the damping ratio represents an underdamped system. - is_valid_azimuthal_quantum_number
- Returns
true when n >= 1 and l < n. - is_valid_coulomb_logarithm
- Returns whether a Coulomb logarithm value is finite and positive.
- is_valid_magnetic_quantum_number
- Returns
true when -l <= m_l <= l. - is_valid_nuclide_numbers
- Validates mass and atomic numbers for a simple nuclide representation.
- is_valid_principal_quantum_number
- Returns
true when n >= 1. - is_valid_quantum_numbers
- Returns
true when the supplied quantum-number combination is valid. - is_valid_restitution
- Returns
true when a restitution coefficient is finite and within [0.0, 1.0]. - is_valid_spin_twice
- Returns
true when the spin projection is one of -1 or 1. - isotropic_intensity
- Computes isotropic intensity from power and distance with
I = P / (4 * pi * r^2). - joules_to_electron_volts
- Converts joules to electron volts using
eV = J / e. - joules_to_mev
- Converts energy in joules to mega-electron-volts.
- kinematic_viscosity
- Computes kinematic viscosity from dynamic viscosity and density.
- kinetic_energy
- kinetic_energy_from_total_and_potential
- Computes kinetic energy from total energy and potential energy using
KE = E_total - U. - kinetic_energy_loss
- Computes the kinetic energy lost between an initial and final state.
- kinetic_energy_loss_fraction
- Computes the fraction of kinetic energy lost between two states.
- lever_arm_from_torque
- Computes the lever arm required to produce a known torque from a force.
- linear_attenuation_from_mass_attenuation
- Computes linear attenuation coefficient from mass attenuation and density.
- linear_kinetic_energy
- Computes translational kinetic energy using
KE = 0.5mv². - linear_momentum
- Computes linear momentum using
p = mv. - lorentz_factor
- Computes the Lorentz factor
γ from a speed magnitude in meters per second. - lorentz_factor_from_beta
- Computes the Lorentz factor
γ = 1 / sqrt(1 - β²) from a non-negative beta magnitude. - lorentz_force_magnitude_perpendicular
- Computes
|F| = |q| * |E + vB| for perpendicular fields along the same scalar direction. - lorentz_force_scalar
- Computes the scalar Lorentz-force convenience relation
F = q(E + vB sin(theta)). - lorentz_force_scalar_degrees
- Computes the scalar Lorentz-force convenience relation with the angle in degrees.
- magnetic_energy_density
- Computes magnetic energy density.
- magnetic_field_around_long_straight_wire
- Computes magnetic flux density around a long straight wire.
- magnetic_field_at_center_of_loop
- Computes magnetic flux density at the center of a circular current loop.
- magnetic_field_energy_density
- Computes magnetic field energy density using
u_B = B² / (2μ0). - magnetic_field_inside_solenoid
- Computes magnetic flux density inside an ideal long solenoid.
- magnetic_flux
- Computes magnetic flux through an area.
- magnetic_flux_degrees
- Computes magnetic flux through an area using an angle in degrees.
- magnetic_flux_density_for_velocity_selector
- Computes magnetic flux density magnitude for a selector using
B = E / v. - magnetic_flux_density_from_electric_field_in_vacuum
- Computes magnetic flux density magnitude in vacuum using
B = E / c. - magnetic_flux_density_from_flux
- Computes magnetic flux density from magnetic flux, area, and orientation.
- magnetic_force_magnitude_on_charge
- Computes the magnitude of magnetic force on a moving charge.
- magnetic_force_on_charge
- Computes magnetic force on a moving charge.
- magnetic_force_on_charge_degrees
- Computes magnetic force on a moving charge using an angle in degrees.
- magnetic_force_on_moving_charge
- Computes magnetic force using
F = qvB sin(theta). - magnetic_force_on_moving_charge_degrees
- Computes magnetic force using
F = qvB sin(theta) with the angle in degrees. - magnetic_force_on_wire
- Computes magnetic force on a current-carrying wire.
- magnetic_force_on_wire_degrees
- Computes magnetic force on a current-carrying wire using an angle in degrees.
- magnetic_pressure
- Computes magnetic pressure.
- mass_attenuation_from_linear_attenuation
- Computes mass attenuation coefficient from linear attenuation and density.
- mass_defect_kg_from_energy
- Computes mass defect in kilograms from energy in joules.
- mass_flow_rate
- Computes mass flow rate from density and volumetric flow rate.
- mass_from_density
- mass_from_momentum
- Computes mass from momentum and velocity using
m = p / v. - mass_from_rest_energy
- Computes rest mass
m = E0 / c² from rest energy in joules. - mass_from_spring_period
- Computes mass from spring constant and period using
m = kT² / 4π². - max_acceleration
- Computes the maximum acceleration using
a_max = Aω². - max_speed
- Computes the maximum speed using
v_max = Aω. - maximum_static_friction
- Computes the maximum available static friction.
- mean_lifetime
- Computes the mean lifetime from a decay constant.
- mechanical_power
- mev_to_joules
- Converts energy in mega-electron-volts to joules.
- minimum_energy_uncertainty
- Computes the minimum energy uncertainty estimate from
delta E >= hbar / (2 * delta t). - minimum_momentum_uncertainty
- Computes the minimum momentum uncertainty estimate from
delta p >= hbar / (2 * delta x). - minimum_position_uncertainty
- Computes the minimum position uncertainty estimate from
delta x >= hbar / (2 * delta p). - minimum_static_friction_coefficient_for_incline
- Computes the minimum static friction coefficient needed to prevent sliding on an incline.
- minimum_time_uncertainty
- Computes the minimum time uncertainty estimate from
delta t >= hbar / (2 * delta E). - moment_2d
- Computes the scalar
z-moment of a planar force about a chosen point. - moment_arm
- Computes the perpendicular moment arm from a lever arm and angle in radians.
- moment_arm_degrees
- Computes the perpendicular moment arm from an angle given in degrees.
- moment_from_force_and_arm
- Computes a moment from a signed force and a signed moment arm.
- momentum
- Computes linear momentum using
p = m * v. - momentum_from_de_broglie_wavelength
- Computes momentum magnitude from a de Broglie wavelength using
p = h / lambda. - momentum_impulse
- Computes impulse from force and elapsed time using
J = F * Δt. - near_surface_potential_energy
- Computes near-surface potential energy from mass, height, and gravitational acceleration.
- net_force_1d
- Computes the net force from a list of scalar forces.
- net_force_2d
- Computes the net force from a list of planar force components.
- net_moment
- Computes the net moment from a slice of scalar moment values.
- net_moment_2d
- Computes the net moment from planar point forces.
- net_torque
- Computes the sum of a slice of torque values.
- net_torque_from_force_lever_pairs
- Computes the net torque for force and lever-arm pairs.
- net_work
- Computes the net work from a slice of work contributions.
- neutron_count
- Computes neutron count from mass number and atomic number.
- normal_force_horizontal_surface
- Computes the normal force on a horizontal surface.
- normal_force_incline
- Computes the normal force on an incline.
- normal_strain
- Computes normal strain from change in length and original length.
- normal_stress
- Computes normal stress from applied force and cross-sectional area.
- nuclei_from_activity
- Computes the number of nuclei from activity and decay constant.
- nucleon_count
- Computes nucleon count from proton and neutron counts.
- observed_frequency_longitudinal
- Computes observed longitudinal Doppler-shifted frequency
f_observed = f_emitted * D. - orbital_radius_from_altitude
- Computes orbital radius from body radius and altitude.
- orbital_radius_from_circular_speed
- Computes the circular orbital radius from circular speed.
- orbital_radius_from_period
- Computes the circular orbital radius from an orbital period.
- oscillation_displacement
- Computes displacement for simple harmonic motion using
x(t) = A * cos(ωt + φ). - oscillation_spring_potential_energy
- Computes spring potential energy using
U = 0.5 * k * x². - oscillator_total_energy
- Computes oscillator total energy using
E = 0.5 * k * A². - parallel_axis_moment_of_inertia
- Applies the parallel-axis theorem using
I = I_cm + md². - parallel_resistance
- Computes the total resistance for resistors in parallel.
- particle_thermal_speed
- Computes a particle thermal speed.
- pendulum_length_from_period
- Computes pendulum length from period using
L = g * (T / 2π)². - perfectly_inelastic_collision_final_velocities_1d
- Computes the final velocities of a perfectly inelastic one-dimensional collision.
- perfectly_inelastic_collision_velocity_1d
- Computes the shared final velocity of a perfectly inelastic one-dimensional collision.
- periapsis_from_semi_major_axis_eccentricity
- Computes periapsis radius from semi-major axis and eccentricity.
- periapsis_speed
- Computes speed at periapsis using the vis-viva equation.
- period_from_angular_frequency
- Computes period from angular frequency using
T = 2π / ω. - period_from_frequency
- Computes period from frequency using
T = 1 / f. - perpendicular_force_component
- Computes the component of a force that acts perpendicular to a lever arm.
- perpendicular_force_component_degrees
- Computes the perpendicular force component from an angle given in degrees.
- photon_energy_from_frequency
- Computes photon energy from frequency using
E = h * f. - photon_energy_from_wavelength
- Computes photon energy from wavelength using
E = h * c / lambda. - photon_flux_density
- Computes photon flux density with
phi = Phi / A. - photon_flux_from_power
- Computes photon flux from power with
Phi = P / E_photon. - photon_momentum_from_energy
- Computes photon momentum from energy using
p = E / c. - photon_momentum_from_wavelength
- Computes photon momentum from wavelength using
p = h / lambda. - plasma_beta
- Computes plasma beta.
- plasma_magnetic_pressure
- Computes magnetic pressure.
- plasma_pressure
- Computes scalar plasma pressure.
- point_mass_moment_of_inertia
- Computes the moment of inertia for a point mass.
- poisson_ratio
- Computes Poisson’s ratio from transverse and axial strain.
- potential_energy
- power_from_current_resistance
- Computes electrical power from current and resistance.
- power_from_voltage_current
- Computes electrical power from voltage and current.
- power_from_voltage_resistance
- Computes electrical power from voltage and resistance.
- poynting_magnitude
- Computes Poynting magnitude in vacuum using
S = EB / μ0. - pressure
- Computes pressure from applied force and cross-sectional area.
- pressure_change_from_bulk_modulus
- Computes pressure change from bulk modulus and volumetric strain.
- proper_length
- Computes proper length
L0 = Lγ from a contracted length L. - proper_time
- Computes proper time
τ = t / γ from dilated coordinate time t. - quality_factor_from_damping_ratio
- Computes quality factor from damping ratio using
Q = 1 / (2ζ). - radians_from_degrees
- Converts degrees to radians.
- radians_from_revolutions
- Converts revolutions to radians.
- rapidity_from_beta
- Computes rapidity
φ = atanh(β) from a signed beta. - recoil_velocity
- Computes recoil velocity assuming the initial total momentum is zero.
- reduced_mass
- Computes reduced mass using
μ = (m1 * m2) / (m1 + m2). - relative_speed
- Computes the relative speed between two one-dimensional bodies.
- relative_velocity
- Computes the signed relative velocity between two one-dimensional bodies.
- relativistic_kinetic_energy
- Computes relativistic kinetic energy
KE = (γ - 1)mc² in joules. - relativistic_momentum
- Computes relativistic momentum
p = γmv. - remaining_fraction_from_decay_constant
- Computes the remaining fraction from a decay constant and elapsed time.
- remaining_fraction_from_half_life
- Computes the remaining fraction from a half-life and elapsed time.
- remaining_quantity_from_decay_constant
- Computes the remaining quantity from an initial quantity, decay constant, and elapsed time.
- remaining_quantity_from_half_life
- Computes the remaining quantity from an initial quantity, half-life, and elapsed time.
- required_shield_thickness
- Computes required shield thickness with
x = ln(I0 / I) / mu. - required_static_friction
- Computes the static friction magnitude required to hold horizontal equilibrium.
- resistance
- Computes resistance from voltage and current using Ohm’s law.
- resistance_from_conductance
- Computes resistance from conductance.
- resonance_angular_frequency_natural
- Computes the natural resonance angular frequency of a spring-mass oscillator.
- rest_energy
- Computes rest energy
E0 = mc² in joules. - rest_mass_from_momentum_speed
- Computes rest mass from relativistic momentum and velocity using
m = p / (γv). - rest_mass_mev_c2
- Returns an approximate rest mass in
MeV/c^2 for kind. - revolutions_from_radians
- Converts radians to revolutions.
- reynolds_number
- Computes Reynolds number from density, velocity, characteristic length, and dynamic viscosity.
- rigidbody_angular_momentum
- Computes angular momentum using
L = Iω. - rigidbody_hollow_sphere_moment_of_inertia
- Computes hollow-sphere moment of inertia using
I = (2 / 3)mr². - rigidbody_point_mass_moment_of_inertia
- Computes point-mass moment of inertia using
I = mr². - rigidbody_rod_moment_of_inertia_about_center
- Computes rod moment of inertia about its center using
I = (1 / 12)mL². - rigidbody_rod_moment_of_inertia_about_end
- Computes rod moment of inertia about one end using
I = (1 / 3)mL². - rigidbody_rotational_kinetic_energy
- Computes rotational kinetic energy using
KE_rot = 0.5Iω². - rigidbody_solid_disk_moment_of_inertia
- Computes solid-disk moment of inertia using
I = 0.5mr². - rigidbody_solid_sphere_moment_of_inertia
- Computes solid-sphere moment of inertia using
I = (2 / 5)mr². - rigidbody_thin_ring_moment_of_inertia
- Computes thin-ring moment of inertia using
I = mr². - rod_moment_of_inertia_about_center
- Computes the moment of inertia of a uniform rod about its center.
- rod_moment_of_inertia_about_end
- Computes the moment of inertia of a uniform rod about one end.
- rotation_angular_acceleration_from_torque
- Computes angular acceleration from torque using
α = τ / I. - rotation_point_mass_moment_of_inertia
- Computes point-mass moment of inertia using
I = mr². - rotation_rod_moment_of_inertia_about_center
- Computes rod moment of inertia about its center using
I = (1 / 12)mL². - rotation_rod_moment_of_inertia_about_end
- Computes rod moment of inertia about one end using
I = (1 / 3)mL². - rotational_kinetic_energy
- Computes rotational kinetic energy using
KE_rot = 0.5 * I * ω². - semi_major_axis_from_apsides
- Computes the semi-major axis from periapsis and apoapsis radii.
- semi_major_axis_from_specific_energy
- Computes the semi-major axis for a bound orbit from specific orbital energy.
- separation_speed_from_restitution
- Computes separation speed from an approach speed and restitution coefficient.
- series_resistance
- Computes the total resistance for resistors in series.
- shear_modulus
- Computes shear modulus from shear stress and shear strain.
- shear_modulus_from_youngs_and_poisson
- Computes shear modulus from Young’s modulus and Poisson’s ratio.
- shear_strain
- Computes engineering shear strain from lateral displacement and height.
- shear_strain_from_modulus
- Computes shear strain from shear stress and shear modulus.
- shear_stress
- Computes shear stress from applied force and loaded area.
- shear_stress_from_modulus
- Computes shear stress from shear modulus and shear strain.
- simple_pendulum_angular_frequency
- Computes small-angle simple pendulum angular frequency using
ω = sqrt(g / L). - simple_pendulum_frequency
- Computes small-angle simple pendulum frequency in cycles per second.
- simple_pendulum_period
- Computes the small-angle simple pendulum period using
T = 2π * sqrt(L / g). - simply_supported_point_load_reactions
- Computes support reactions for a simply supported beam with one point load.
- simply_supported_uniform_load_reactions
- Computes support reactions for a simply supported beam with a uniform load.
- solid_disk_moment_of_inertia
- Computes solid-disk moment of inertia using
I = 0.5mr². - solid_sphere_moment_of_inertia
- Computes solid-sphere moment of inertia using
I = (2 / 5)mr². - source_mass_from_gravitational_parameter
- Computes the source mass from a standard gravitational parameter.
- specific_activity
- Computes specific activity from activity and mass.
- specific_orbital_energy
- Computes specific orbital energy.
- speed_from_beta
- Computes the speed magnitude
v = βc in meters per second. - speed_from_permittivity_permeability
- Computes propagation speed from permittivity and permeability using
v = 1 / sqrt(εμ). - speed_from_rapidity
- Computes signed velocity
v = c * tanh(φ) from rapidity. - spin
- Returns the spin for
kind. - spring_angular_frequency
- Computes spring angular frequency using
ω = sqrt(k / m). - spring_constant_from_period
- Computes spring constant from mass and period using
k = 4π²m / T². - spring_frequency
- Computes spring frequency in cycles per second.
- spring_period
- Computes spring period using
T = 2π * sqrt(m / k). - spring_potential_energy
- Computes the spring potential energy stored at a displacement.
- spring_work
- Computes work done by an ideal spring force over a displacement interval.
- standard_weight
- Computes weight under conventional standard gravity.
- statics_is_rotational_equilibrium
- Checks whether a moment system is in rotational equilibrium.
- statistics
- Returns the particle statistics implied by the modeled spin.
- strain_from_youngs_modulus
- Computes strain from stress and Young’s modulus.
- stress_from_youngs_modulus
- Computes stress from Young’s modulus and axial strain.
- tangential_acceleration
- Computes tangential acceleration using
a_t = αr. - tangential_speed
- Computes tangential speed using
v = ωr. - tenth_value_layer
- Computes tenth-value layer with
TVL = ln(10) / mu. - thin_ring_moment_of_inertia
- Computes thin-ring moment of inertia using
I = mr². - torque
- Computes torque from a force and lever arm.
- torque_at_angle
- Computes torque when the applied force meets the lever arm at an angle in radians.
- torque_at_angle_degrees
- Computes torque when the applied force meets the lever arm at an angle in degrees.
- torques_from_force_lever_pairs
- Converts force and lever-arm pairs into torque values.
- total_effective_dose
- Sums pre-weighted equivalent doses into a total effective dose.
- total_energy
- Computes total relativistic energy
E = γmc² in joules. - total_kinetic_energy
- Computes total kinetic energy using
KE_total = 0.5mv² + 0.5Iω². - total_kinetic_energy_1d
- Computes the total kinetic energy of two one-dimensional bodies.
- total_momentum
- Computes the total momentum of a slice of momentum values.
- total_plasma_pressure
- Computes total scalar plasma pressure.
- transmitted_fraction
- Computes transmitted fraction with
T = e^(-mu * x). - transverse_strain_from_poisson_ratio
- Computes transverse strain from Poisson’s ratio and axial strain.
- two_body_total_momentum
- Computes the total momentum of two moving bodies using
p_total = m1v1 + m2v2. - velocity
- Computes velocity for simple harmonic motion using
v(t) = -Aω * sin(ωt + φ). - velocity_addition
- Computes relativistic velocity addition
u = (v + w) / (1 + vw / c²). - velocity_after_impulse
- Computes final velocity after an impulse using
v_final = v_initial + J / m. - velocity_from_flow_rate
- Computes velocity from volumetric flow rate and area.
- velocity_from_momentum
- Computes velocity from momentum and mass using
v = p / m. - velocity_selector_speed
- Computes selector speed using
v = E / B. - vis_viva_speed
- Computes orbital speed from the vis-viva equation.
- voltage
- Computes voltage from current and resistance using Ohm’s law.
- volume
- Computes occupied volume from mass and density.
- volume_strain
- Computes volumetric strain from change in volume and original volume.
- volumetric_flow_rate
- Computes volumetric flow rate from area and flow velocity.
- wavelength_from_photon_energy
- Computes wavelength from photon energy using
lambda = h * c / E. - weight
- work
- work_against_gravity
- Computes work done against gravity near a surface.
- work_at_angle
- Computes mechanical work when the force is applied at an angle to the displacement.
- work_at_angle_degrees
- Computes mechanical work when the applied-force angle is given in degrees.
- work_by_friction
- Computes work done by kinetic friction.
- work_by_gravity
- Computes work done by gravity near a surface.
- work_from_force_samples
- Approximates work from aligned force and displacement samples.
- work_from_kinetic_energy_change
- Computes net work from the change in kinetic energy.
- youngs_modulus
- Computes Young’s modulus from stress and strain.
- youngs_modulus_from_shear_and_poisson
- Computes Young’s modulus from shear modulus and Poisson’s ratio.