Symplyphysics¶
Physics laws implemented as code. Based on SymPy Python library.
Autogenerated from Symplyphysics project.
Contents:
- Formulas
- Physical symbols
- Astronomy (Symbols)
- Basic (Symbols)
any_quantitytimeperiodmassmolar_massworkenergy_densityspectral_energy_densityenergyspecific_energypowerradius_of_curvaturedensitylinear_densityintensitywhole_numberpositive_numbernonnegative_numbernumber_densityparticle_countangleprobabilityfractional_changeexponential_decay_constantcharacteristic_lengthmolar_volume
- Chemistry (Symbols)
- Classical mechanics (Symbols)
forcetensionspeedaccelerationpositioneuclidean_distancedistancedistance_to_origindistance_to_axisorthogonal_distancelengthradiusdiametersemimajor_axissemiminor_axisthicknessareaarc_lengthangular_speedangular_frequencyangular_accelerationangular_distanceangular_wavenumberwavelengthdamping_ratiovolumeimpulsephase_speedgroup_speedpressuretemporal_frequencysound_intensity_levelrotational_inertiaquality_factormomentummechanical_energykinetic_energypotential_energymass_flow_ratevolumetric_flow_ratestiffnesscomplianceyoung_modulusphase_shiftphasefriction_coefficientheighttorquetorsion_stiffnessbulk_moduluspoisson_ratioengineering_normal_straindeformationstrainstressmach_numberdynamic_viscositydiffusion_fluxdegrees_of_freedomangular_momentumlatitudelongitudesector_speedkepler_constantsurface_tensiondynamic_pressuremechanical_efficiencyhydrostatic_pressurefroude_numberspeed_of_soundnusselt_numberreynolds_numbershear_stressflow_speeddamping_constantshear_modulusengineering_shear_strain
- Electrodynamics (Symbols)
admittanceelectrical_conductancesusceptanceelectrical_impedancewave_impedanceelectromotive_forcemagnetic_fluxabsolute_permittivityrelative_permittivityabsolute_permeabilityrelative_permeabilitycapacitancechargevoltagecurrentelectrical_resistanceelectric_dipole_momentelectric_field_strengthvolumetric_charge_densitysurface_charge_densityelectric_fluxmagnetic_flux_densityelectric_potentialpower_factorelectrical_resistivityinductanceelectric_time_constantelectrical_reactancecurrent_densityemissivitymagnetic_momentelectric_displacementattenuation_coefficientmagnetic_field_strengthelectrical_conductivitycircuit_gaindiode_constantdirect_permeability_coefficientattenuationsurge_impedancereflection_coefficientstanding_wave_ratiophase_constantpropagation_constantdielectric_loss_tangent
- Nuclear Physics (Symbols)
geometric_bucklingmultiplication_factorinfinite_multiplication_factoreffective_multiplication_factorneutron_diffusion_areaneutron_fluxmaterial_bucklingfast_non_leakage_probabilitythermal_non_leakage_probabilityfast_fission_factorresonance_escape_probabilityfast_absorption_fission_probabilitythermal_absorption_fission_probabilitythermal_utilization_factorfast_utilizationneutron_fermi_agethermal_fission_factorhalf_lifemacroscopic_cross_sectionneutron_diffusion_coefficientmigration_areareproduction_factor
- Optics (Symbols)
- Quantum Mechanics (Symbols)
- Relativistic mechanics (Symbols)
- Thermodynamics (Symbols)
temperatureadiabatic_indexheat_capacitymolar_heat_capacitythermal_expansion_coefficientthermodynamic_compressibilitythermal_resistancethermal_conductivitythermal_insulancecompressibility_factorpartition_functionboltzmann_factorentropychemical_potentialgibbs_energyenthalpyhelmholtz_free_energyinternal_energythermal_wavelengthheatthermal_efficiencystatistical_weightrelative_humiditymean_free_pathsutherland_constantprandtl_numbergrashof_numberkinematic_viscositythermal_diffusivityattractive_forces_parameterexcluded_volume_parameterheat_transfer_coefficient
- Physical constants
standard_conditions_temperaturestandard_laboratory_temperatureelectron_rest_massbohr_radiushydrogen_ionization_energysolar_massearth_massboltzmann_constantmolar_gas_constantspeed_of_lightvacuum_permittivityvacuum_permeabilityelementary_chargehbarplanckavogadro_constantacceleration_due_to_gravitystefan_boltzmann_constantrichardson_constantrydberg_frequencywien_displacement_constantgravitational_constanthubble_constantzero_point_luminositysun_luminosityfaraday_constantvacuum_impedance
- Mathematics
- Fields
- Geometry
- Classical Mechanics
- Conservation Laws (Classical Mechanics)
- Dynamics
- Energy (Dynamics)
- Force (Dynamics)
- Acceleration from force and mass (vector)
- Acceleration is force over mass
- Braking path via speed and friction force
- Conservative force is gradient of potential energy
- Damping force is proportional to velocity
- Force is derivative of momentum
- Force is derivative of momentum (vector)
- Friction force from normal force
- Impulse is integral of force over time
- Net force is sum of individual forces
- Net force vector is sum of forces
- Normal force via pressure and vector area
- Reaction force equals action force
- Gravity (Dynamics)
- Acceleration due to gravity via gravity force and centripetal acceleration
- Easterly deviation from plumbline of falling bodies
- Falling body displacement
- Free fall acceleration from height
- Gravitational potential energy
- Gravitational force from mass and distance
- Potential energy from mass and height
- Relative acceleration from force and acceleration due to gravity
- Southerly deviation from plumbline of falling bodies
- Relative Motion (Dynamics)
- Rotational Motion (Dynamics)
- Angular momentum is position cross linear momentum
- Angular momentum is rotational inertia times angular speed
- Kinetic energy from rotational inertia and angular speed
- Kinetic energy via angular momentum and angular velocity
- Rotational work is torque times angular distance
- Torque is angular momentum derivative
- Torque of twisting force
- Torque via force and radial distance
- Torque via rotational inertia and angular acceleration
- Translational Motion (Dynamics)
- Fundamentals (Classical Mechanics)
- Kinematics
- Centers (Kinematics)
- General Motion (Kinematics)
- Projectile Motion (Kinematics)
- Relative Motion (Kinematics)
- Absolute velocity of arbitrary motion
- Acceleration due to non-uniform rotation
- Acceleration of transfer between relative frames
- Centrifugal acceleration via centripetal acceleration
- Coriolis acceleration via relative velocity and angular velocity
- Velocity of transfer between reference frames
- Velocity relative to reference frame
- Rotational Motion (Kinematics)
- Rotational Inertia
- Rotational inertia about axis and through center of mass
- Rotational inertia in terms of Cartesian integral
- Rotational inertia in terms of a cylindrical integral
- Rotational inertia is additive
- Rotational inertia of a particle
- Slab about perpendicular axis through center
- Solid disk about central axis
- Thin rod about axis through center perpendicular to length
- Angular acceleration is angular speed derivative
- Angular position is arc length over radius
- Angular position via constant angular acceleration and time
- Angular position via constant angular speed and time
- Angular speed is angular distance derivative
- Angular speed via constant angular acceleration and time
- Average angular speed is angular distance over time
- Centripetal acceleration via angular speed and radius
- Centripetal acceleration via cross product
- Centripetal acceleration via vector rejection
- Linear displacement is angular displacement cross radius
- Rotational Inertia
- Translational Motion (Kinematics)
- Orbital Mechanics
- Angle of rotation during gravitational maneuver
- Area rate of change is proportional to angular momentum
- Average potential energy via average kinetic energy
- Corrected planet period squared is proportional to cube of semimajor axis
- Eccentricity of orbit via orbit parameters
- First escape velocity
- Kepler’s constant via attracting body mass
- Maximum angle of rotation during gravitational maneuver
- Orbital speed from semimajor axis and planet mass
- Planet period squared is proportional to cube of semimajor axis
- Potential energy of radial planetary motion
- Radial kinetic energy plus potential energy is constant
- Radius of geostationary orbit
- Second escape velocity
- Semimajor axis of orbit via mass and speed
- Semimajor axis via Kepler’s constant and total energy
- Semiminor axis of elliptical orbit via orbit parameters
- Third cosmic speed from orbital and second cosmic speed
- Total energy is negative average kinetic energy
- Springs (Classical Mechanics)
- Statics
- Two Body System
- Oscillations
- Mechanical Oscillations
- Damped Oscillations
- Forced Mechanical Oscillations
- Physical Pendulum
- Spring
- Torsion Pendulum
- Natural Oscillations
- Quality Factor
- Period from angular frequency
- Temporal frequency from period
- Temporal frequency is number of events per unit time
- Mechanical Oscillations
- Waves
- Acoustic Waves (Waves)
- Doppler Effect (Waves)
- Standing Waves
- Stretched String (Waves)
- Wave Interference (Waves)
- Wave Propagation (Waves)
- Angular wavenumber is inverse wavelength
- Radiant exitance is radiant flux emitted per unit area
- Radiation intensity from energy, area, and time
- General solution to wave equation in one dimension
- Wave equation in one dimension
- Continuum Mechanics
- Acoustic Waves (Continuum Mechanics)
- Elasticity
- Energy (Elasticity)
- Material Properties
- Strain
- Stress
- Fluid Mechanics
- Hydraulic Press
- Hydrostatics
- Incompressible Flow
- Dynamic pressure from density and flow speed
- Efflux speed via height
- Efflux speed via hydrostatic pressure and density
- Inner pressure is constant
- Inner pressure is sum of pressures
- Pressure difference at pipe ends from dynamic viscosity and flow rate
- Pressure of liquid in vessel moving horizontally
- Pressure of liquid in vessel moving vertically
- Volume flux is constant
- Similarity Parameters
- Supersonic Flow
- Surface Effects
- Transport Properties
- Special Relativity
- Fundamentals (Special Relativity)
- Relativistic Dynamics (Special Relativity)
- Energy and Momentum (Special Relativity)
- Relativistic energy—momentum relation
- Relativistic energy via relativistic mass
- Total energy via momentum and rest mass
- Relativistic kinetic energy via rest mass and Lorentz factor
- Relativistic mass moment
- Relativistic momentum via rest mass and velocity
- Relativistic momentum via rest mass and speed
- Force and Acceleration (Special Relativity)
- Obsolete Concepts (Special Relativity)
- Energy and Momentum (Special Relativity)
- Relativistic Kinematics
- Lorentz Transformations
- Relativistic Effects (Relativistic Kinematics)
- Relativistic Velocity Addition
- Rocket Mechanics (Special Relativity)
- General Relativity
- Electromagnetism
- Circuits
- Alternating Current (Circuits)
- Components (Circuits)
- Capacitors
- Couplers
- Attenuation of three link microwave attenuator
- Admittance of rectangular loop coupler
- Total gain of transistor amplifier
- Impedance of Wilkinson microstrip divider
- Section length of multistage transformer
- Relative operating bandwidth of quarter-wave transformer
- Resistor resistance in Wilkinson divider
- Transient attenuation of separate loop coupler with cascade connection
- Wave impedance of even mode of Lange coupler
- Wave impedance of odd mode of Lange coupler
- Wave impedance of Lange coupler
- Diodes
- Current from voltage and diode constant in vacuum diode
- Current from voltage and triode constant in vacuum triode
- Diode constant for parallel-plane vacuum diode
- Diode constant of cylindrical diode
- Direct permeability coefficient of triode with flat electrodes
- Internal resistance of vacuum diode
- Limit operating frequency of vacuum diode
- Charge density in diode
- Steepness of volt-ampere characteristic of vacuum diode
- Voltage of equivalent diode for pentode
- Equivalent diode voltage for tetrode
- Equivalent diode voltage for triode
- Filters
- Transmission coefficient approximation of low-pass filter
- Band pass Chebyshev filter order from distortion and frequency
- Butterworth filter order from distortion and frequency
- Filter order from distortion and frequency
- High pass Chebyshev filter from distortion and frequency
- Low-pass Chebyshev filter order from distortion and frequencies
- Inductors
- Resistors
- Resonators
- Coupling parameter of resonator from quality factor
- Coupling parameter of resonator from resistance
- Instantaneous energy of resonator
- Quality factor of loaded resonator from circuit parameters
- Quality resonator of loaded resonator from quality factors
- Quality factor of resonator
- Quality factor of empty rectangular resonator for traverse electric waves
- Quality factor of filled rectangular resonator
- Resonant frequency of rectangular resonator
- Resonant frequency of ring resonator
- Varactors
- Direct Current (Circuits)
- Fundamentals (Circuits)
- Transient Analysis
- Transmission Lines
- Coplanar Lines
- Effective permittivity of coplanar transmission line when distance is greater than thickness
- Effective permittivity of coplanar transmission line when distance is less than thickness
- Wave impedance of coplanar line when hyperbolic sine ratio squared is between \(0\) and \(\frac{1}{2}\)
- Wave impedance of coplanar line when length to distance ratio squared is between \(\frac{1}{2}\) and \(1\)
- Microstrip Lines
- Attenuation coefficient in dielectric substate of microstrip line
- Attenuation coefficient in metal of microstrip line when width is greater than thickness
- Attenuation coefficient in microstrip metal when thickness is greater than width times \(2 \pi\)
- Attenuation coefficient in microstrip metal when thickness is less than width times \(2 \pi\)
- Effective permittivity of microstrip line when width is greater than thickness
- Effective permittivity of microstrip line when width is less than thickness
- Effective permittivity of microstrip line from frequency
- Effective width of microstrip line when width is greater than thickness
- Effective width of microstrip line when width is less than thickness
- Inductance of microstrip line strip
- Resistance of microstrip line
- Short circuit inductance of microstrip line
- Surge impedance of microstrip line from frequency
- Standing wave ratio from reflection coefficient
- Standing wave ratio from voltage
- Hybrid parameters matrix equation
- Impedance matrix equation
- Impedances of π-type circuit of transmission line
- Impedances of T-type circuit of transmission line
- Input impedance from transmission matrix
- Input impedance of lossless transmission line
- Input impedance of lossy transmission line
- Reflection coefficient from ratio of average power to incident power
- Standing wave ratio from ratio of average power to incident power
- Reflection coefficient from load and surge impedance
- Scattering matrix equation
- Scattering matrix to transmission matrix
- Admittance matrix equation
- Transmission matrix equation
- Transmission matrix for parallel load in line
- Transmission matrix for serial load in line
- Transmission matrix of lossless transmission line
- Transmission matrix of lossy transmission line
- Transmission matrix of π-type matrix
- Transmission matrix of T-type circuit
- Surge impedance of microstrip line when effective width is greater than substrate thickness
- Surge impedance of microstrip line when effective width is less than substrate thickness
- Coplanar Lines
- Waveguides
- Attenuation coefficient in dielectric
- Attenuation coefficient in dielectric in rectangular waveguide
- Attenuation coefficient in metal
- Attenuation coefficient in metal in rectangular waveguide for transverse electric waves
- Attenuation coefficient in metal in rectangular waveguide for transverse magnetic waves
- Wave impedance in rectangular waveguide for transverse electric waves
- Characteristic resistance of rectangular waveguide for transverse magnetic waves
- Critical wavelength in rectangular waveguide
- Group speed of wave in rectangular waveguide
- Maximum electric field strength of main wave in rectangular waveguide
- Maximum voltage in coaxial line
- Phase speed of wave in rectangular waveguide
- Power carried by coaxial waveguide
- Power carried by main wave of rectangular waveguide
- Specific capacitance of coaxial waveguide
- Specific conductivity of coaxial waveguide
- Specific inductance of coaxial waveguide
- Specific resistance of coaxial waveguide
- Surface resistance of metal
- Wave resistance of coaxial waveguide
- Wavelength in rectangular waveguide
- Conservation Laws (Electromagnetism)
- Corona Discharge
- Electrodynamics
- Charge Transport (Electrodynamics)
- Constitutive Relations
- Dynamics (Electromagnetism)
- Electromotive Force
- Maxwell’s Equations
- Electrostatics
- Capacitance
- Charged Plane
- Charged Sphere
- Electric Dipole
- Electric dipole moment is charge times displacement
- Electric dipole moment is charge times distance
- Electric dipole moment of electrically neutral system
- Electric field due to dipole on the dipole axis
- Electric field due to dipole (Vector)
- Force acting on dipole in non-uniform electric field
- Potential energy of electric dipole in uniform electric field
- Torque due to electric dipole moment in uniform electric field
- Electric Flux
- Point Charge
- Electric field due to point charge
- Electric field is force over test charge
- Electric field is force over test charge (Vector)
- Electrostatic force between two charges
- Electrostatic force via charges and distance
- Electrostatic potential due to point charge
- Electrostatic potential energy of two charges via distance
- Electrostatic potential is work to bring from reference point over charge
- Voltage
- Fundamentals (Electromagnetism)
- Magnetostatics
- Charged Particle Motion
- Coil
- Current Loop
- Inductance
- Magnetic Dipole
- Magnetic Flux
- Straight Wire
- Space Charge
- Circuits
- Electromagnetic waves
- Blackbody Radiation
- Doppler Effect (Electromagnetic Waves)
- Relativistic Effects (Electromagnetic Waves)
- Wave Energy (Electromagnetic Waves)
- Wave Propagation (Electromagnetic Waves)
- Optics
- Geometrical Optics
- Invariants (Geometrical Optics)
- Lenses
- Lens focus from object and image
- Linear magnification from distance to object and distance to image
- Linear magnification from object height and image height
- Optical power from focus distance
- Optical power from thin lens radii and refractive indices
- Optical power of spherical lens from refractive indices and distances
- Mirrors
- Prisms
- Refraction (Geometrical Optics)
- Telescopes
- Wave Optics
- Geometrical Optics
- Astronomy
- Celestial Mechanics
- Observational Astronomy
- Observational Cosmology
- Positional Astronomy
- Stellar Evolution
- Nuclear Physics
- Buckling (Nuclear Physics)
- Geometric buckling for uniform cylinder
- Geometric buckling for uniform parallelepiped
- Geometric buckling for uniform slab
- Geometric buckling for uniform sphere
- Geometric buckling from multiplication factors and diffusion area
- Geometric buckling from macroscopic cross sections and diffusion coefficient
- Geometric buckling from neutron flux
- Material buckling from material cross sections and diffusion coefficient
- Neutron flux for uniform cylinder
- Neutron flux for uniform parallelepiped
- Neutron flux for uniform slab
- Neutron flux for uniform sphere
- Diffusion area from diffusion coefficient and absorption cross section
- Diffusion equation from neutron flux
- Effective multiplication factor from infinite multiplication factor and probabilities
- Fast fission factor from resonance escape probability
- Fast non-leakage probability from Fermi age and geometric buckling
- Half life decay
- Infinite multiplication factor formula
- Infinite multiplication factor from macroscopic cross sections
- Macroscopic cross section from mean free path
- Macroscopic cross section from microscopic cross section and number density
- Macroscopic transport cross section from macroscopic scattering cross section
- Migration area from diffusion length and Fermi age
- Average cosine of scattering angle from mass number
- Diffusion coefficient from macroscopic scattering cross section
- Reproduction factor from macroscopic cross sections in fuel
- Resonance escape probability from resonance absorption integral
- Thermal non-leakage probability from diffusion area and geometric buckling
- Thermal utilization factor from macroscopic absorption cross sections
- Buckling (Nuclear Physics)
- Chemistry
- Quantity Relations
- Quantum Physics
- Bohr Model
- Fundamentals
- Light Interaction
- Photons (Quantum Physics)
- Quantum Harmonic Oscillator
- Schrödinger Equation
- Condensed Matter
- Crystallography
- Electrical Properties (Condensed Matter)
- Electronic Emission
- Gas Plasma
- Interaction Potentials
- Ionization
- Magnetron
- Boundary of thermalization zone of atomized atoms in magnetron
- Distance of greatest convergence of particles in magnetron
- Energy transfer coefficient for elastic scattering in magnetron
- Etch rate of target in magnetron
- Interaction cross section in Coulomb’s interaction model
- Interaction cross section in elastic interaction model
- Interaction cross section in model of hard spheres
- Interaction cross section in recharge model
- Number of collisions of particle with gas in magnetron
- Semiconductors
- Thermodynamics (Condensed Matter)
- Transport Phenomena
- Thermodynamics
- Chemical Thermodynamics
- Conservation Laws (Thermodynamics)
- Continuum Thermodynamics
- Dielectric Thermodynamics
- Equation of state
- Enthalpy change via entropy change and electric field change
- Enthalpy of dielectrics
- Free energy change via temperature change and electric displacement change
- Gibbs energy change via temperature change and electric displacement change
- Gibbs energy of dielectrics
- Internal energy change via heat and electric displacement change
- Dielectric Thermodynamics
- Equations of State
- Compressibility Factor
- Dietirici Model
- Ideal Gas Model
- Van der Waals Model
- Critical van der Waals molar volume
- Critical van der Waals pressure
- Critical van der Waals temperature
- Dimensionless van der Waals equation
- Reduced van der Waals pressure
- Reduced van der Waals temperature
- Reduced van der Waals volume
- Van der Waals equation
- Van der Waals molar internal energy
- Van der Waals second virial coefficient
- Virial Expansion
- Heat Engines
- Heat Transfer
- Phase Transitions
- Thermodynamic Response Functions
- Thermodynamic Compressibility
- Heat Capacity
- Heat capacity ratio
- Heat is heat capacity times temperature change
- Isobaric molar heat capacity of ideal gas via adiabatic index
- Isochoric and isobaric heat capacities of homogeneous substance
- Isochoric and isobaric heat capacities of ideal gas
- Isochoric molar heat capacity of ideal gas via adiabatic index
- Isochoric molar heat capacity of ideal gas via degrees of freedom
- Thermal Expansion
- Thermodynamic Potentials
- Definitions (Thermodynamic Potentials)
- Chemical potential is particle count derivative of enthalpy
- Chemical potential is particle count derivative of free energy
- Chemical potential is particle count derivative of Gibbs energy
- Chemical potential is particle count derivative of internal energy
- Enthalpy is internal energy plus pressure energy
- Gibbs energy via enthalpy
- Helmholtz free energy via internal energy
- Differentials (Thermodynamic Potentials)
- Euler Relations
- Ideal Gas (Thermodynamic Potentials)
- Identities (Thermodynamic Potentials)
- Legendre Transform (Thermodynamic Potentials)
- Maxwell Relations
- Properties (Thermodynamic Potentials)
- Definitions (Thermodynamic Potentials)
- Work and Heat
- Statistical Physics
- Classical Statistics
- Kinetic Theory
- Average kinetic energy of ideal gas from temperature
- Gas mixture pressure from partial pressures
- Internal energy change of ideal gas via temperature
- Internal energy of ideal gas via temperature
- Mean free path of particles in gaseous medium
- Mean free path of random motion
- Number of impacts on the wall from area and speed
- Pressure from number density and kinetic energy
- Maxwell—Boltzmann Statistics
- Kinetic Theory
- Statistical Ensembles
- Occupancies
- Quantum Statistics
- Relativistic Statistics
- Classical Statistics