- ->L-state
- ->local
- ->state
- acceleration
- acceleration-tuple
- accelerations
- coordinate
- coordinate-tuple
- coordinates
- Dt
- Dt-procedure
- Euler-Lagrange-operator
- F->C
- find-path
- Gamma
- Gamma-bar
- generalized-LE
- L-axisymmetric-top
- L-central-polar
- L-central-rectangular
- L-coupled-harmonic
- L-free-particle
- L-harmonic
- L-Kepler-polar
- L-pendulum
- L-rectangular
- L-sliding-pend
- L-two-particle
- L-uniform-acceleration
- L3-central
- Lagrange-equations
- Lagrange-equations-1
- Lagrange-equations-first-order
- Lagrange-equations-operator
- Lagrange-interpolation-function
- Lagrangian
- Lagrangian->acceleration
- Lagrangian->energy
- Lagrangian->power-loss
- Lagrangian->state-derivative
- Lagrangian-action
- LE
- linear-interpolants
- literal-Lagrangian-state
- local-state-derivative
- make-Lagrangian
- make-path
- momentum-tuple
- osculating-path
- p->r
- parametric-path-action
- path->state-path
- polar->rectangular
- Q
- Qdot
- Qdotdot
- qv->local-path
- r->p
- r->s
- Rayleigh-dissipation
- rectangular->polar
- rectangular->spherical
- s->r
- spherical->rectangular
- state->n-dof
- state->q
- state->qddot
- state->qdot
- state->t
- T3-spherical
- time
- velocities
- velocity
- velocity-tuple
emmy.mechanics.lagrange
->L-stateclj/s
(->L-state t q qdot & derivs)Given a time t, coordinate tuple (or scalar) q, velocity tuple (or scalar)
qdot and any number of additional higher-order derivative tuples (or
scalars), returns a 'Local tuple', i.e., the state expected by a Lagrangian.
Given a time `t`, coordinate tuple (or scalar) `q`, velocity tuple (or scalar) `qdot` and any number of additional higher-order derivative tuples (or scalars), returns a 'Local tuple', i.e., the state expected by a Lagrangian.
accelerationclj/s
(acceleration local)Returns the acceleration element of a local tuple (by convention, the fourth element).
See coordinate for more detail.
Returns the acceleration element of a local tuple (by convention, the fourth element). See [[coordinate]] for more detail.
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.)
coordinate 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.) [[coordinate]] returns the `q` element, which is expected to be a mapping from time to a structure of coordinates.
F->Cclj/s
(F->C F)Accepts a coordinate transformation F from a local tuple to a new coordinate
structure, and returns a function from local -> local that applies the
transformation directly.
F->C handles local tuples of arbitrary length.
Accepts a coordinate transformation `F` from a local tuple to a new coordinate structure, and returns a function from `local -> local` that applies the transformation directly. [[F->C]] handles local tuples of arbitrary length.
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.
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).
L-central-polarclj/s
(L-central-polar m U)Consider planar motion in a central force field, with an arbitrary potential,
U, depending only on the radius. The generalized coordinates are polar.
Consider planar motion in a central force field, with an arbitrary potential, `U`, depending only on the radius. The generalized coordinates are polar.
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.
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.
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)
L-sliding-pendclj/s
(L-sliding-pend m1 m2 l g)Pendulum of mass m2 and length b, hanging from a support of mass m1 that is free to move horizontally (from Groesberg, Advanced Mechanics, p. 72)
Pendulum of mass m2 and length b, hanging from a support of mass m1 that is free to move horizontally (from Groesberg, Advanced Mechanics, p. 72)
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
Lagrange-equations-1clj/s
Alias for Lagrange-equations-first-order.
Alias for [[Lagrange-equations-first-order]].
Lagrange-equations-operatorclj/s
Alias for [[Euler-lagrange-operator]].
Alias for [[Euler-lagrange-operator]].
Lagrange-interpolation-functionclj/s
(Lagrange-interpolation-function ys xs)Given ys (a sequence of function values) and xs (an equal-length sequence
of function inputs), returns a [[emmy.polynomial/Polynomial]] instance
guaranteed to pass through all supplied xs and ys.
The contract for inputs is that (map vector xs ys) should return a sequence
of pairs of points.
Given `ys` (a sequence of function values) and `xs` (an equal-length sequence of function inputs), returns a [[emmy.polynomial/Polynomial]] instance guaranteed to pass through all supplied `xs` and `ys`. The contract for inputs is that `(map vector xs ys)` should return a sequence of pairs of points.
Lagrangianclj/s
(Lagrangian)(Lagrangian n)Returns a function signature for a Lagrangian with n degrees of freedom (or an unrestricted number if n is not given).
Useful for constructing Lagrangian literal functions.
Returns a function signature for a Lagrangian with n degrees of freedom (or an unrestricted number if n is not given). Useful for constructing Lagrangian literal functions.
Lagrangian->accelerationclj/s
(Lagrangian->acceleration L)(Lagrangian->acceleration L dissipation-fn)Lagrangian->state-derivativeclj/s
(Lagrangian->state-derivative L)(Lagrangian->state-derivative L dissipation-fn)Optionally takes a dissipation function.
Optionally takes a dissipation function.
Lagrangian-actionclj/s
(Lagrangian-action L q t1 t2)(Lagrangian-action L q t1 t2 integration-opts)LEclj/s
Alias for [[Euler-lagrange-operator]].
Alias for [[Euler-lagrange-operator]].
local-state-derivativeclj/s
(local-state-derivative L)The state derivative of a Lagrangian is a function carrying a state tuple to its time derivative.
Alias for the non-dissipative, single-arity version
of Lagrangian->state-derivative.
The state derivative of a Lagrangian is a function carrying a state tuple to its time derivative. Alias for the non-dissipative, single-arity version of [[Lagrangian->state-derivative]].
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.
p->rclj/s
(p->r tqv)SICM p. 47. Polar to rectangular coordinates of state.
SICM p. 47. Polar to rectangular coordinates of state.
parametric-path-actionclj/s
(parametric-path-action Lagrangian t0 q0 t1 q1)SICM p. 23
SICM p. 23
timeclj/s
(time local)Extract the time slot from a state tuple.
See coordinate for more detail.
Extract the time slot from a state tuple. See [[coordinate]] for more detail.
velocityclj/s
(velocity local)Returns the velocity element of a local tuple (by convention, the third element).
See coordinate for more detail.
Returns the velocity element of a local tuple (by convention, the third element). See [[coordinate]] for more detail.
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