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sicmutils.mechanics.lagrange


->localclj/s


coordinateclj/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

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
raw docstring

coordinate-tupleclj/s

(coordinate-tuple & xs)

Dtclj/s

(Dt F)

Euler-Lagrange-operatorclj/s

(Euler-Lagrange-operator L)

F->Cclj/s

(F->C F)

find-pathclj/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.

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

Gammaclj/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 takes a path function (from time to coordinates) to a state
function (from time to local tuple).
raw docstring

Gamma-barclj/s

(Gamma-bar f)

L-central-polarclj/s

(L-central-polar m U)

L-central-rectangularclj/s

(L-central-rectangular m U)

L-free-particleclj/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.

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.
raw docstring

L-harmonicclj/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.

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.
raw docstring

L-rectangularclj/s

(L-rectangular m V)

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

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

L-uniform-accelerationclj/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

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

Lagrange-equationsclj/s

(Lagrange-equations Lagrangian)

Lagrange-equations-first-orderclj/s

(Lagrange-equations-first-order L)

Lagrange-interpolation-functionclj/s

(Lagrange-interpolation-function ys xs)

Lagrangian->accelerationclj/s

(Lagrangian->acceleration L)

Lagrangian->energyclj/s

(Lagrangian->energy L)

Lagrangian->state-derivativeclj/s

(Lagrangian->state-derivative L)

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

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

Lagrangian-actionclj/s

(Lagrangian-action L q t1 t2)

linear-interpolantsclj/s

(linear-interpolants x0 x1 n)

make-pathclj/s

(make-path t0 q0 t1 q1 qs)

SICM p. 23n

SICM p. 23n
raw docstring

osculating-pathclj/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.

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.
raw docstring

p->rclj/s

(p->r [_ [r φ]])

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

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

parametric-path-actionclj/s

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

SICM p. 23

SICM p. 23
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qv->state-pathclj/s

(qv->state-path q v)

s->rclj/s

(s->r [_ [r θ φ] _])

SICM p. 83

SICM p. 83
raw docstring

state->tclj/s

(state->t s)

Extract the time slot from a state tuple

Extract the time slot from a state tuple
raw docstring

velocityclj/s

(velocity local)

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

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

velocity-tupleclj/s


Γclj/s


Γ-barclj/s

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