Spherical pendulum
This example models a spherical pendulum. The pivot point is modeled using a Spherical
joint, this lets the pendulum rotate in three directions. The pendulum rod is modeled using a FixedTranslation
, a component without inertial properties, and the mass of the tip is modeled using a Body
. To model a rod with inertial properties, see, e.g., BodyShape
or BodyCylinder
, In this example, we choose the joint to be the root (joints are often better root objects than bodies).
using Multibody
using ModelingToolkit
using Plots
using JuliaSimCompiler
using OrdinaryDiffEq
t = Multibody.t
D = Differential(t)
world = Multibody.world
systems = @named begin
joint = Spherical(state=true, isroot=true, phi = 1, phid = 3, radius=0.1, color=[1,1,0,1])
bar = FixedTranslation(r = [0, -1, 0])
body = Body(; m = 1, isroot = false, r_cm=[0.1, 0, 0])
end
connections = [connect(world.frame_b, joint.frame_a)
connect(joint.frame_b, bar.frame_a)
connect(bar.frame_b, body.frame_a)]
@named model = ODESystem(connections, t, systems = [world; systems])
ssys = structural_simplify(IRSystem(model))
prob = ODEProblem(ssys, [], (0, 5))
sol = solve(prob, Rodas4())
@assert SciMLBase.successful_retcode(sol)
plot(sol, idxs = [body.r_0...])
3D animation
Multibody.jl supports automatic 3D rendering of mechanisms, we use this feature to illustrate the result of the simulation below:
import GLMakie
Multibody.render(model, sol; filename = "spherical.gif") # Use "spherical.mp4" for a video file