fgtp_engine · Compute action integral S

Read the equation

This relation defines action integral S in the source section “fgtp_engine · Compute action integral S”. Integrates contributions over the variable and bounds stated in the expression; the measure and domain must come from this source. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read action integral S as the quantity being defined or updated by this relation.

2. Integrates contributions over the variable and bounds stated in the expression; the measure and domain must come from this source.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

• This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.

Original context

    /// Compute Hamiltonian H = T + V + E_field
    double compute_hamiltonian(const EnergyState& state) const noexcept;

    /// Compute Lagrangian L = T - V
    double compute_lagrangian(double kinetic, double potential) const noexcept;

    /// Compute action integral S = ∫ L dt (over trajectory)
    double compute_action(
        const std::vector<EnergyState>& trajectory,
        double dt = 1.0
    ) const noexcept;

    /// Principle of least action: minimize S
    std::vector<double> optimize_trajectory(
        const std::vector<double>& start,
        const std::vector<double>& end,
        size_t steps = 100

Compute action integral S = ∫ L dt (over trajectory)

Related builds