MultiPendulum

MultiPendulumMotion::new(lengths, masses, angles, seconds) solves a chain of point masses on massless rods released at rest, a double pendulum with two links, from the Lagrangian with Runge-Kutta at 240 steps a second. Keep it in the video, built once. Over 10 s a chaotic double pendulum keeps its energy within 1e-6 on the steps. Sampled between two steps, the blended state is off by about 1e-3, which does not show. state(t), positions(t) (meters from the pivot, y up) and energy(t) give the numbers. MultiPendulum draws it from pivot, scale units per meter. With trail the last bob leaves a trail, sampled like TracedPath, over the last trail_time seconds. Gallery scenes: MultiPendulum, and ChaosFan: 24 double pendulums released 0.002 rad apart, which swing as one and then fan out.

MultiPendulum 4 sPlayUnmuteCopy render command

ChaosFan 6.5 sPlayUnmuteCopy render command

use fframes_kit::prelude::*;

struct Video {
    chain: MultiPendulumMotion,
}

impl Video {
    fn new() -> Self {
        Self {
            chain: MultiPendulumMotion::new(&[1.4, 1.1], &[1.0, 1.0], &[2.2, 2.6], 10.0),
        }
    }

    fn figure<'a>(&'a self, ui: &mut Ui<'a, '_, '_>) -> Svgr<'a> {
        ui.show(MultiPendulum {
            motion: Some(&self.chain),
            pivot: (0.0, 1.0),
            trail_time: Some(2.0),
            ..ui.defaults()
        })
    }
}

API

Components are plain structs. Set the fields you need and fill the rest with ..ui.defaults(): the defaults below come from the current theme (theme. values are fields of Theme).

MultiPendulum

Field	Type	Default	Description
motion	Option<&MultiPendulumMotion>	None	The simulated chain to draw, built once in the video’s constructor; None draws nothing.
pivot	(f64, f64)	(0.0, 2.5)	Where the first rod hangs from, in units of ui.space.
scale	f64	1.0	Units of ui.space per meter.
delay	f32	0.0	Seconds after the local start before the chain is released.
time_scale	f32	1.0	Speed of the motion over local time; 2 runs twice as fast, 1 is real time.
bob_radius	f32	18.0	Radius of the bobs in pixels.
trail	bool	true	Leaves a trail behind the last bob.
trail_time	Option<f32>	Some(3.0)	Seconds of the trail that stay visible; None keeps all of it.
color	Color	theme.colors.text	Colour of the rods, the pivot and the ceiling.
bob_color	Color	theme.colors.accent	Colour of the bobs.
trail_color	Color	theme.colors.highlight	Colour of the trail.
stroke_width	f32	theme.stroke.regular	Width of the rods, the ceiling and the trail in pixels.
enter	Option<EnterAnim>	None	How the ceiling draws in; None shows it from the start.
exit	Option<ExitAnim>	None	How the ceiling leaves at the end of the container; None stays.
parts_enter	Option<FadeIn>	None	How the rods, bobs and trail fade in; None for none.
parts_exit	Option<FadeOut>	None	How the rods, bobs and trail fade out before the end; None for none.

Feature physics · Source