sicmutils.mechanics.lagrange — net.littleredcomputer/sicmutils 0.14.0-SNAPSHOT

->local clj/s

coordinate clj/s

(coordinate local)

A convenience function on local tuples. A local tuple describes the state of a system at a particular time: [t, q, D q, D^2 q] representing time, position, velocity (and optionally acceleration etc.) Returns the q element, which is expected to be a mapping from time to a structure of coordinates

coordinate-tuple clj/s

(coordinate-tuple & xs)

Dt clj/s

(Dt F)

Euler-Lagrange-operator clj/s

(Euler-Lagrange-operator L)

F->C clj/s

(F->C F)

find-path clj/s

(find-path Lagrangian t0 q0 t1 q1 n & {:keys [observe]})

SICM p. 23. The optional parameter values is a callback which will report intermediate points of the minimization.

Gamma clj/s

(Gamma q)

(Gamma q n)

Gamma takes a path function (from time to coordinates) to a state function (from time to local tuple).

Gamma-bar clj/s

(Gamma-bar f)

L-central-polar clj/s

(L-central-polar m U)

L-central-rectangular clj/s

(L-central-rectangular m U)

L-free-particle clj/s

(L-free-particle mass)

The lagrangian of a free particle of mass m. The Lagrangian returned is a function of the local tuple. Since the particle is free, there is no potential energy, so the Lagrangian is just the kinetic energy.

L-harmonic clj/s

(L-harmonic m k)

The Lagrangian of a simple harmonic oscillator (mass-spring system). m is the mass and k is the spring constant used in Hooke's law. The resulting Lagrangian is a function of the local tuple of the system.

L-rectangular clj/s

(L-rectangular m V)

Lagrangian for a point mass on with the potential energy V(x, y)

L-uniform-acceleration clj/s

(L-uniform-acceleration m g)

The Lagrangian of an object experiencing uniform acceleration in the negative y direction, i.e. the acceleration due to gravity

Lagrange-equations clj/s

(Lagrange-equations Lagrangian)

Lagrange-equations-first-order clj/s

(Lagrange-equations-first-order L)

Lagrange-interpolation-function clj/s

(Lagrange-interpolation-function ys xs)

Lagrangian->acceleration clj/s

(Lagrangian->acceleration L)

Lagrangian->energy clj/s

(Lagrangian->energy L)

Lagrangian->state-derivative clj/s

(Lagrangian->state-derivative L)

The state derivative of a Lagrangian is a function carrying a state tuple to its time derivative.

Lagrangian-action clj/s

(Lagrangian-action L q t1 t2)

linear-interpolants clj/s

(linear-interpolants x0 x1 n)

make-path clj/s

(make-path t0 q0 t1 q1 qs)

SICM p. 23n

osculating-path clj/s

(osculating-path state0)

Given a state tuple (of finite length), reconstitutes the initial segment of the Taylor series corresponding to the state tuple data as a function of t. Time is measured beginning at the point of time specified in the input state tuple.

p->r clj/s

(p->r [_ [r φ]])

SICM p. 47. Polar to rectangular coordinates of state.

parametric-path-action clj/s

(parametric-path-action Lagrangian t0 q0 t1 q1)

SICM p. 23

qv->state-path clj/s

(qv->state-path q v)

s->r clj/s

(s->r [_ [r θ φ] _])

SICM p. 83

state->t clj/s

(state->t s)

Extract the time slot from a state tuple

velocity clj/s

(velocity local)

See coordinate: this returns the velocity element of a local tuple (by convention, the 2nd element).

velocity-tuple clj/s

Γ clj/s

Γ-bar clj/s