Class HamiltonianMechanics

java.lang.Object
org.episteme.natural.physics.HamiltonianMechanics
public class HamiltonianMechanics extends Object
Hamiltonian mechanics - phase space formulation of classical mechanics.

Hamiltonian: H = Σpᵢq̇ᵢ - L Hamilton's equations: q̇ = ∂H/∂p, ṗ = -∂H/∂q

*

Reference:
Hamilton, W. R. (1834). On a General Method in Dynamics. Philosophical Transactions of the Royal Society.

Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Constructor Summary

    Constructors
    Constructor
    Description
    HamiltonianMechanics()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    static Real
    hamiltonian(Real kineticEnergy, Real potentialEnergy)
    Hamiltonian: H = T + V (total energy in conservative system)
    static Real
    hamiltonianEMField(Real momentum, Real charge, Real vectorPotential, Real mass, Real scalarPotential)
    Hamiltonian for charged particle in EM field: H = (p - qA)²/(2m) + qφ (Simplified scalar version)
    static Real
    hamiltonianFreeParticle(Real momentum, Real mass)
    Hamiltonian for free particle: H = p²/(2m)
    static Real
    hamiltonianFromLagrangian(Real momentum, Real velocity, Real lagrangian)
    Hamiltonian from Lagrangian: H = pq̇ - L
    static Real
    hamiltonianHarmonicOscillator(Real momentum, Real mass, Real springConstant, Real position)
    Hamiltonian for harmonic oscillator: H = p²/(2m) + ½kx²
    static Real
    phaseSpaceVolume(Real[] q, Real[] p)
    Phase space volume element: dΓ = Πᵢ dqᵢ dpᵢ (Preserved by Hamiltonian flow - Liouville's theorem)
    static Real
    poissonBracket1D(Real dfDq, Real dfDp, Real dgDq, Real dgDp)
    Poisson bracket: {f,g} = Σᵢ(∂f/∂qᵢ ∂g/∂pᵢ - ∂f/∂pᵢ ∂g/∂qᵢ) Simplified 1D version

    Methods inherited from class Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • HamiltonianMechanics

      public HamiltonianMechanics()

  • Method Details

    • hamiltonianFreeParticle

      public static Real hamiltonianFreeParticle(Real momentum, Real mass)
      Hamiltonian for free particle: H = p²/(2m)

    • hamiltonian

      public static Real hamiltonian(Real kineticEnergy, Real potentialEnergy)
      Hamiltonian: H = T + V (total energy in conservative system)

    • hamiltonianFromLagrangian

      public static Real hamiltonianFromLagrangian(Real momentum, Real velocity, Real lagrangian)
      Hamiltonian from Lagrangian: H = pq̇ - L

    • hamiltonianHarmonicOscillator

      public static Real hamiltonianHarmonicOscillator(Real momentum, Real mass, Real springConstant, Real position)
      Hamiltonian for harmonic oscillator: H = p²/(2m) + ½kx²

    • poissonBracket1D

      public static Real poissonBracket1D(Real dfDq, Real dfDp, Real dgDq, Real dgDp)
      Poisson bracket: {f,g} = Σᵢ(∂f/∂qᵢ ∂g/∂pᵢ - ∂f/∂pᵢ ∂g/∂qᵢ) Simplified 1D version

    • phaseSpaceVolume

      public static Real phaseSpaceVolume(Real[] q, Real[] p)
      Phase space volume element: dΓ = Πᵢ dqᵢ dpᵢ (Preserved by Hamiltonian flow - Liouville's theorem)

    • hamiltonianEMField

      public static Real hamiltonianEMField(Real momentum, Real charge, Real vectorPotential, Real mass, Real scalarPotential)
      Hamiltonian for charged particle in EM field: H = (p - qA)²/(2m) + qφ (Simplified scalar version)