emmy.mechanics.hamilton — org.mentat/emmy 0.31.0

*validate-Legendre-transform?* clj/s

If true, the state passed to the fn returned by Legendre-transform is checked for correctness. If false errors may occur. See the code body for more detail.

Defaults to false.

->H-state clj/s

(->H-state t q p)

Given a time t, coordinate tuple (or scalar) q and momentum tuple (or scalar) p, returns a 'Hamiltonian state tuple', i.e., the state expected by a Hamiltonian.

canonical-H? clj/s

(canonical-H? C H)

canonical-K? clj/s

(canonical-K? C K)

canonical-transform? clj/s

(canonical-transform? C)

canonical? clj/s

(canonical? C H Hprime)

p.324

compatible-H-state? clj/s

(compatible-H-state? s)

Returns true if s is compatible for contraction with a proper H-state, false otherwise.

compositional-canonical? clj/s

(compositional-canonical? C H)

p.324

D-phase-space clj/s

(D-phase-space H)

F->CH clj/s

(F->CH F)

A transformation of configuration coordinates F to a procedure implementing a transformation of phase-space coordinates (p. 320)

F->CT clj/s

Alias for F->CH.

F->K clj/s

(F->K F)

flow-derivative clj/s

(flow-derivative H)

the flow derivative generalizes the Lie derivative to allow for time dependent H and F --- computes the 'time' derivative of F along the flow specified by H

flow-transform clj/s

(flow-transform H delta-t)

The generalization of Lie-transform to include time dependence.

H-central clj/s

(H-central m V)

H-central-polar clj/s

(H-central-polar m V)

H-harmonic clj/s

(H-harmonic m k)

H-rectangular clj/s

(H-rectangular m V)

H-state->L-state clj/s

(H-state->L-state H)

H-state->matrix clj/s

(H-state->matrix s)

H-state? clj/s

(H-state? s)

Returns true if the supplied state is

• of type emmy.structure/up

• contains three elements of time, coordinate and momentum of either of the following type shapes:

(up <number> <number> <number>)
(up <number> (up <number>*) (down <number>*))

If structural, the dimension of the coordinate and momentum tuples must match.

Hamilton-equations clj/s

(Hamilton-equations Hamiltonian)

Hamiltonian clj/s

(Hamiltonian n)

Returns function signature for a Hamiltonian with n degrees of freedom (or an unrestricted number if n is not given).

Useful for constructing Hamiltonian literal functions.

Hamiltonian->Lagrangian clj/s

Hamiltonian->state-derivative clj/s

(Hamiltonian->state-derivative H)

iterated-map clj/s

(iterated-map f n)

f is a function of (x y continue fail), which calls continue with the values of x' y' that follow x y in the mapping.

Returns a map of the same shape that iterates the iterated map n times before invoking the continuation, or invokes the fail continuation if the inner map fails.

J-func clj/s

(J-func DHs)

J-matrix clj/s

(J-matrix n)

n == degrees of freedom

L-state->H-state clj/s

(L-state->H-state L)

Lagrangian->Hamiltonian clj/s

Legendre-transform clj/s

Lie-transform clj/s

(Lie-transform H t)

p. 428, the Lie transform is just the time-advance operator using the Lie derivative (see Hamiltonian.scm).

linear-function->multiplier clj/s

(linear-function->multiplier F argument)

literal-Hamiltonian-state clj/s

(literal-Hamiltonian-state n-dof)

make-Hamiltonian clj/s

(make-Hamiltonian kinetic-energy potential-energy)

matrix->H-state clj/s

(matrix->H-state m s)

momenta clj/s

Alias for momentum.

momentum clj/s

(momentum H-state)

Returns the momentum element of a local Hamiltonian state tuple (by convention, the third element).

multiplicative-transpose clj/s

(multiplicative-transpose s)

P clj/s

Alias for momentum.

phase-space-derivative clj/s

Alias for Hamiltonian->state-derivative, for compatibility with 1st edition of SICM.

Phi clj/s

(Phi A)

Phi* clj/s

(Phi* A)

Poisson-bracket clj/s

(Poisson-bracket f g)

polar-canonical clj/s

(polar-canonical alpha)

p.327

polar-canonical-inverse clj/s

(polar-canonical-inverse alpha)

qp->H-state-path clj/s

(qp->H-state-path q p)

qp-canonical? clj/s

(qp-canonical? C H)

Tests that K yields a canonical transformation if the C is symplectic. (The qp-canonical? code is really a symplectic test without factoring out the Hamiltonian.)

qp-submatrix clj/s

(qp-submatrix m)

standard-map clj/s

(standard-map K)

standard-map-inverse clj/s

(standard-map-inverse K)

state->p clj/s

Alias for momentum.

state->qp clj/s

(state->qp s)

Given a hamiltonian state, returns a emmy.structure/up containing the coordinate and momentum components.

symplectic-matrix? clj/s

(symplectic-matrix? M)

p. 334

symplectic-transform? clj/s

(symplectic-transform? C)

p. 334

symplectic-two-form clj/s

(symplectic-two-form zeta1 zeta2)

symplectic-unit clj/s

(symplectic-unit n)

p. 334 (used, but not defined there)

symplectic? clj/s

(symplectic? C)

Symplectic test in terms of matrices

T-func clj/s

(T-func s)

time-independent-canonical? clj/s

(time-independent-canonical? C)

p.326

transpose-function clj/s

(transpose-function A)

two-particle-center-of-mass clj/s

(two-particle-center-of-mass m0 m1)

two-particle-center-of-mass-canonical clj/s

(two-particle-center-of-mass-canonical m0 m1)