Pendulum and EnergyBars

PendulumMotion::new(length, angle0, seconds) swings a pendulum from rest without friction; PendulumMotion::damped(length, angle0, damping, seconds) slows it. Pendulum draws it hanging from pivot, with the reach of the swing as a dashed arc and the angle from the vertical. EnergyBars shows kinetic energy, potential energy and their sum in pixels. Feed it motion.energy(t, mass) at the pendulum’s clock, and one bar empties while the other fills, with the total level (or falling, with damping). Gallery scenes: Pendulum, EnergyBars.

Pendulum 6 sPlayUnmuteCopy render command

EnergyBars 6 sPlayUnmuteCopy render command

use std::sync::OnceLock;

use fframes_kit::prelude::*;

fn figure<'a>(ui: &mut Ui<'a, '_, '_>) -> Svgr<'a> {
    static MOTION: OnceLock<PendulumMotion> = OnceLock::new();
    let motion = MOTION.get_or_init(|| PendulumMotion::new(2.5, 0.9, 6.0));
    let delay = 0.5;
    let t = f64::from((ui.seconds() - delay).max(0.0));
    let (kinetic, potential) = motion.energy(t, 1.0);
    let pendulum = ui.show(Pendulum {
        motion: Some(motion),
        pivot: (-2.5, 2.6),
        delay,
        ..ui.defaults()
    });
    let bars = ui.show(EnergyBars {
        kinetic,
        potential,
        max: motion.energy(0.0, 1.0).1,
        ..ui.defaults()
    });
    svgr!(<g>{pendulum}{bars}</g>)
}

EnergyBars also accepts values directly. This example exchanges energy between the bars while keeping their total at one joule; positions and dimensions are in pixels.

use fframes_kit::prelude::*;

fn bars<'a>(ui: &mut Ui<'a, '_, '_>) -> Svgr<'a> {
    let kinetic = f64::from(ui.seconds()).sin().powi(2);
    ui.show(EnergyBars {
        kinetic,
        potential: 1.0 - kinetic,
        max: 1.0,
        x: 590.0,
        y: 860.0,
        bar_width: 180.0,
        gap: 100.0,
        height: 560.0,
        ..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).

Pendulum

A pendulum hanging from pivot (units of ui.space, scale units per meter) that swings as motion says, from delay seconds after the local start. With arc the swing’s reach is a dashed arc, with angle_label the angle from the vertical is written next to the pivot. The ceiling and the arc draw with enter, the rod and bob fade with parts_enter. Without motion nothing is drawn.

Field	Type	Default	Description
motion	Option<&PendulumMotion>	None	The simulated swing to draw, built once in the video’s constructor; None draws nothing.
pivot	(f64, f64)	(0.0, 2.5)	Where the 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 pendulum 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	28.0	Radius of the bob in pixels.
arc	bool	true	Draws the reach of the swing as a dashed arc.
angle_label	bool	true	Writes the angle from the vertical, in degrees, beside the pivot.
color	Color	theme.colors.text	Colour of the rod, the pivot, the ceiling and the angle label.
bob_color	Color	theme.colors.accent	Colour of the bob.
guide_color	Color	theme.colors.muted	Colour of the dashed arc, the rest line and the angle arc.
stroke_width	f32	theme.stroke.regular	Width of the rod and the ceiling in pixels.
enter	Option<EnterAnim>	None	How the ceiling and the arc draw in; None shows them from the start.
exit	Option<ExitAnim>	None	How the ceiling and the arc leave at the end of the container; None stays.
parts_enter	Option<FadeIn>	None	How the rod and bob fade in; None for none.
parts_exit	Option<FadeOut>	None	How the rod and bob fade out before the end; None for none.

Feature physics · Source

EnergyBars

Bars of kinetic energy, potential energy and their sum, standing on (x, y) (pixels, the bottom left corner) and height pixels tall at max joules. Give them the values of the current frame, for example from PendulumMotion::energy at the same clock as the figure, and the exchange shows as one bar shrinking while the other grows with the total level. The frames draw with enter, the bars and labels fade with parts_enter.

Field	Type	Default	Description
kinetic	f64	0.0	Kinetic energy in joules shown by the first bar.
potential	f64	0.0	Potential energy in joules shown by the second bar.
max	f64	1.0	Joules at which a bar is height pixels tall; larger values are clamped.
x	f32	1400.0	Left edge of the first bar, in pixels of the canvas.
y	f32	820.0	Bottom edge of the bars (their baseline), in pixels of the canvas.
bar_width	f32	80.0	Width of each bar in pixels.
gap	f32	40.0	Pixels between one bar and the next.
height	f32	420.0	Height in pixels of a full bar and its frame.
labels	bool	true	Writes KE, PE and E at the foot of the three bars.
kinetic_color	Color	theme.colors.accent	Colour of the kinetic bar and its share of the total.
potential_color	Color	theme.colors.highlight	Colour of the potential bar and its share of the total.
total_color	Color	theme.colors.text	Colour of the labels.
frame_color	Color	theme.colors.muted	Colour of the outline frames of the bars.
enter	Option<EnterAnim>	None	How the frames draw in; None shows them from the start.
exit	Option<ExitAnim>	None	How the frames leave at the end of the container; None stays.
parts_enter	Option<FadeIn>	None	How the bars and labels fade in; None for none.
parts_exit	Option<FadeOut>	None	How the bars and labels fade out before the end; None for none.

Feature physics · Source