Double pendulum

This page is a visualization of a toy example for the article Time-dependent metrics and connections.

Frictionless double pendulum with time-dependent masses.

Parameters

Constants

L_{1} =

L_{2} =

Evolution of masses

{\dot{M}}_{1} (t) =

{\dot{M}}_{2} (t) =

Initial State

Initial conditions

t_{0} =

M_{1} (t_{0}) =

M_{2} (t_{0}) =

θ_{1} (t_{0}) =

ω_{1} (t_{0}) =

θ_{2} (t_{0}) =

ω_{2} (t_{0}) =

The trajectories of masses in a double pendulum are described by the geodesics of the metric defined by the kinetic energy.

In the case of the time-dependent masses, the associated masses become also time-dependent.

In our work we define the notion of geodesics of a time-dependent metrics, and we see that the equations given by those geodesics (plus the potential energy) give the actual trajectories of the system, in a similar fashion time-dependent metrics do.

Technicalities

For this visualization, in addition to JS for the input/output bindings, the actual realtime computations are provided by the system's driver which programmed in C. I ported it to web using WebAssembly.

For the integrator, I used GSL which at some point I compiled to WASM. Concretely, it uses the implementation of the Runge-Kutta-Fehlberg (4, 5) method.