emmy.mathbox.physics — org.mentat/emmy-viewers 0.3.1

Server-side rendering functions for the components declared in the emmy.mathbox.components.physics namespace.

comet clj/s

(comet {:keys [initial-state] :as opts})

Returns a fragment that renders a point that trails its historical positions out behind it in a glowing tail.

Required arguments:

• :atom: atom holding a JS array representing some state. :state->xyz will transform this into xyz coordinates to draw.

Optional arguments:

• :state->xyz: function from the contents of :atom to [x y z] coordinates.

• :initial-state: structure in the shape of the state required by :state->xyz', used if :state->xyz' is a function that needs to be compiled (ie not a quoted literal function).

• :length: the length of the comet tail. Defaults to 16.

• :size: size of the comet. Defaults to 10.

• :opacity: opacity of the leading point of the comet. Defaults to 1.0.

• :color: color of each curve. This can be a three.js Color object or any valid input to its constructor.

• :z-order: z-order of the comet.

• :z-index: zIndex of the comet. Defaults to 0.

• :z-bias: zBias of the comet. Defaults to 0.

geodesic clj/s

(geodesic {:keys [xform x0 v0] :as opts})

Returns a fragment that plots a geodesic curve over the parametric surface defined by :xform, starting from initial position :x0 with initial velocity :v0. The geodesic curve is generated by integrating a system of ordinary differential equations forward for steps steps of dt each.

Required arguments:

• :xform: function of the form (fn [[u v]] [<x> <y> <z>])

• :x0: starting position of the geodesic in [u v] coordinates.

• :v0: starting velocity of the geodesic in [udot vdot].

See ode-curve for a description of all supported optional options.

hamiltonian-curve clj/s

(hamiltonian-curve {:keys [H] :as opts})

Returns a fragment that plots a curve by integrating a system of ordinary differential equations generated from the Hamiltonian passed via :H forward from the initial input state initial-state for steps steps of dt each.

Required arguments:

• :H: function of the form (fn [[t q p]] <energy>)

• :initial-state: the initial input vector to :H.

See ode-curve for a description of all supported optional options.

hamiltonian-phase-vectors clj/s

(hamiltonian-phase-vectors {:keys [H] :as opts})

Returns a fragment that plots a curve at each point on a grid by integrating a system of ordinary differential equations generated from the Hamiltonian passed via :H forward from the initial input state :initial-state for :steps steps of :dt each.

Each point is initialized by swapping out :x-idx and :v-idx in :initial-state with the $(x, \vdot{x})$ coordinates of the phase portrait.

Required arguments:

• :H: function of the form (fn [[t q p]] <energy>)

• :initial-state: the initial input vector to :H.

See phase-vectors for a description of all supported optional options.

lagrangian-curve clj/s

(lagrangian-curve {:keys [L] :as opts})

Returns a fragment that plots a curve by integrating a system of ordinary differential equations generated from the Lagrangian passed via :L forward from the initial input state initial-state for steps steps of dt each.

Required arguments:

• :L: function of the form (fn [[t q qdot]] <energy>)

• :initial-state: the initial input vector to :L.

See ode-curve for a description of all supported optional options.

lagrangian-phase-vectors clj/s

(lagrangian-phase-vectors {:keys [L] :as opts})

Returns a fragment that plots a curve at each point on a grid by integrating a system of ordinary differential equations generated from the Lagrangian passed via :L forward from the initial input state :initial-state for :steps steps of :dt each.

Each point is initialized by swapping out :x-idx and :v-idx in :initial-state with the $(x, \vdot{x})$ coordinates of the phase portrait.

Required arguments:

• :L: function of the form (fn [[t q qdot]] <energy>)

• :initial-state: the initial input vector to :L.

See phase-vectors for a description of all supported optional options.

ode-curve clj/s

(ode-curve {:keys [initial-state] :as opts})

Returns a fragment that plots a curve by integrating a system of ordinary differential equations represented by f' forward from the initial input state initial-state for steps steps of dt each.

Required arguments:

• :f': function of the form (fn [[y0 y1 ...]] [<y0'> <y1'> ...]) that returns a vector of the derivatives of each input variable.

• :initial-state: the initial input vector to :f'.

Optional arguments:

• :state->xyz: function of the form (fn [[y0 y1 ...]] [<x> <y> <z>]), responsible for transforming each integrated state into a 3D point. Defaults to identity.

• :simplify? if true, the compiler will attempt to simplify the body of :state->xyz and :f'. false by default.

• :steps: the number of :dt-spaced steps for the integrator to take. Defaults to 1000.

• :dt: the distance of each evenly spaced step taken by the integrator. Defaults to 3e-2.

• :epsilon: error tolerance passed along to odex-js. Defaults to 1e-5.

• :width: width of the curve. Defaults to 4.

• :start? if true, renders an arrow at the start of the curve. Defaults to false.

• :end? if true, renders an arrow at the end of the curve. Defaults to false.

• :arrow-size: size of the arrows toggled by :start? and :end?. Defaults to 6.

• :opacity: opacity of the curve. Defaults to 1.0.

• :color: color of the curve. This can be a three.js Color object or any valid input to its constructor.

• :z-order: z-order of the curve.

• :z-index: zIndex of the curve. Defaults to 0.

• :z-bias: zBias of the curve. Defaults to 0.

phase-vectors clj/s

(phase-vectors {:keys [initial-state] :as opts})

In-progress attempt at a proper phase portrait component.

Returns a fragment that plots a curve at each point on a grid by integrating a system of ordinary differential equations represented by f' forward from the initial input state :initial-state for :steps steps of :dt each.

Each point is initialized by swapping out :x-idx and :v-idx in :initial-state with the $(x, \vdot{x})$ coordinates of the phase portrait.

NOTE that this is kind of weird, and only works for second-order ODEs that have been transformed. It might be that we want to allow this, but also just call :f if the user doesn't supply :v-idx, for more general ODEs.

Required arguments:

• :f': function of the form (fn [[y0 y1 ...]] [<y0'> <y1'> ...]) that returns a vector of the derivatives of each input variable.

• :initial-state: the initial input vector to :f'.

Optional arguments:

• :x-idx: index of the coordinate position in the state. Defaults to 1.

• :v-idx index of the derivative of :x-idx in the state. Defaults to 2.

• :steps: the number of :dt-spaced steps for the integrator to take. Defaults to 10.

• :dt: the distance of each evenly spaced step taken by the integrator. Defaults to 3e-2.

• :epsilon: error tolerance passed along to odex-js. Defaults to 1e-5.

• :width: width of each curve. Defaults to 2.

• :start? if true, renders an arrow at the start of the curve. Defaults to false.

• :end? if true, renders an arrow at the end of the curve. Defaults to true.

• :arrow-size: size of the arrows toggled by :start? and :end?. Defaults to 5.

• :opacity: opacity of each curve. Defaults to 1.0.

• :color: color of each curve. This can be a three.js Color object or any valid input to its constructor.

• :z-order: z-order of the phase portrait.

• :z-index: zIndex of the phase portrait. Defaults to 0.

• :z-bias: zBias of the phase portrait. Defaults to 0.

routhian-curve clj/s

(routhian-curve {:keys [R] :as opts})

Returns a fragment that plots a curve by integrating a system of ordinary differential equations generated from the Routhian passed via :R forward from the initial input state initial-state for steps steps of dt each.

Required arguments:

• :R: function of the form (fn [[t q qdot-or-p]] <energy>)

• :initial-state: the initial input vector to :R.

See ode-curve for a description of all supported optional options.

routhian-phase-vectors clj/s

(routhian-phase-vectors {:keys [R] :as opts})

Returns a fragment that plots a curve at each point on a grid by integrating a system of ordinary differential equations generated from the Routhian passed via :R forward from the initial input state :initial-state for :steps steps of :dt each.

Each point is initialized by swapping out :x-idx and :v-idx in :initial-state with the $(x, \vdot{x})$ coordinates of the phase portrait.

Required arguments:

• :R: function of the form (fn [[t q qdot-or-p]] <energy>)

• :initial-state: the initial input vector to :R.

See phase-vectors for a description of all supported optional options.