- *validate-Legendre-transform?*
- ->H-state
- canonical-H?
- canonical-K?
- canonical-transform?
- canonical?
- compatible-H-state?
- compositional-canonical?
- D-phase-space
- F->CH
- F->CT
- F->K
- flow-derivative
- flow-transform
- H-central
- H-central-polar
- H-harmonic
- H-rectangular
- H-state->L-state
- H-state->matrix
- H-state?
- Hamilton-equations
- Hamiltonian
- Hamiltonian->Lagrangian
- Hamiltonian->state-derivative
- iterated-map
- J-func
- J-matrix
- L-state->H-state
- Lagrangian->Hamiltonian
- Legendre-transform
- Lie-transform
- linear-function->multiplier
- literal-Hamiltonian-state
- make-Hamiltonian
- matrix->H-state
- momenta
- momentum
- multiplicative-transpose
- P
- phase-space-derivative
- Phi
- Phi*
- Poisson-bracket
- polar-canonical
- polar-canonical-inverse
- qp->H-state-path
- qp-canonical?
- qp-submatrix
- standard-map
- standard-map-inverse
- state->p
- state->qp
- symplectic-matrix?
- symplectic-transform?
- symplectic-two-form
- symplectic-unit
- symplectic?
- T-func
- time-independent-canonical?
- transpose-function
- two-particle-center-of-mass
- two-particle-center-of-mass-canonical
emmy.mechanics.hamilton
*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.
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-stateclj/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.
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.
compatible-H-state?clj/s
(compatible-H-state? s)Returns true if s is compatible for contraction with a proper H-state, false
otherwise.
Returns true if `s` is compatible for contraction with a proper H-state, false otherwise.
F->CHclj/s
(F->CH F)A transformation of configuration coordinates F to a procedure implementing a transformation of phase-space coordinates (p. 320)
A transformation of configuration coordinates F to a procedure implementing a transformation of phase-space coordinates (p. 320)
flow-derivativeclj/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
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-transformclj/s
(flow-transform H delta-t)The generalization of Lie-transform to include time dependence.
The generalization of Lie-transform to include time dependence.
H-state?clj/s
(H-state? s)Returns true if the supplied state is
-
of type
emmy.structure/up -
contains three elements of
time,coordinateandmomentumof 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.
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.
Hamiltonianclj/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.
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.
iterated-mapclj/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.
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.
Lie-transformclj/s
(Lie-transform H t)p. 428, the Lie transform is just the time-advance operator using the Lie derivative (see Hamiltonian.scm).
p. 428, the Lie transform is just the time-advance operator using the Lie derivative (see Hamiltonian.scm).
momentumclj/s
(momentum H-state)Returns the momentum element of a local Hamiltonian state tuple (by convention, the third element).
Returns the momentum element of a local Hamiltonian state tuple (by convention, the third element).
phase-space-derivativeclj/s
Alias for Hamiltonian->state-derivative, for compatibility with
1st edition of SICM.
Alias for [[Hamiltonian->state-derivative]], for compatibility with 1st edition of SICM.
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.)
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.)
state->qpclj/s
(state->qp s)Given a hamiltonian state, returns a emmy.structure/up containing the
coordinate and momentum components.
Given a hamiltonian state, returns a [[emmy.structure/up]] containing the coordinate and momentum components.
symplectic-unitclj/s
(symplectic-unit n)p. 334 (used, but not defined there)
p. 334 (used, but not defined there)
symplectic?clj/s
(symplectic? C)Symplectic test in terms of matrices
Symplectic test in terms of matrices
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