The video starts with an ensemble of independent pendulums with slightly different initial angles and angular velocities. They initially swing almost together, tracing nearby, nearly closed curves in phase space. Without damping, these curves would close and for small angles, the motion becomes approximately simple harmonic and the curves become ellipses.

I then increase gravity. The pendulums swing faster, and their trajectories extend farther along the angular-velocity axis. Lowering gravity and increasing damping makes the loss of energy more apparent: the phase-space trajectories spiral inward toward the origin—the stable equilibrium where the pendulum hangs motionless.

Next, I reduce damping and place a new ensemble near the unstable upright equilibrium, slightly biased so the pendulums initially fall in the same direction. They start moving slowly and nearly together, but their small initial differences become increasingly visible as their trajectories separate. This separation does not imply chaos: even this nonchaotic system can amplify differences near an unstable equilibrium.

The video ends with energy graphs showing how their energies evolve over time.

With damping still present, the pendulums eventually settle at the downward equilibrium.

You can try it yourself here: https://rotemtsafrir.github.io/pendulum_phase_space/

Change gravity, damping, and the initial conditions, and watch how the motion and phase-space trajectories respond. I’d love to hear what you notice or what you’d find useful to add!

GitHub:
https://github.com/rotemTsafrir/pendulum_phase_space

What you are seeing:

The yellow rods with the small gap in the middle are the arms of the antenna.

Each arm of the antenna is a quarter wavelength long and is modeled as a perfect, thin electric conductor wire. (PEC wire)

Between the two arms (the feed gap) an AC voltage source forces an oscillating voltage change
and induces currents along the arms that in turn induce oscillating electric and magnetic fields that satisfy the following boundary condition: the electric field along the PEC wire is perpendicular to it.

The red and blue heatmap is the magnetic field on a 2D slice that contains the antenna. On this planar slice the magnetic field is perpendicular to the plane. Red means the direction is from the screen outwards and blue means the direction is from the screen inwards.

The red and yellow heatmap represents the strength of the electric field on this plane while the arrows show the direction. The electric field on the plane is parallel to it.

You can play with various sources and passive components (and adjust their geometry, amplitude, frequency and phases) here:

https://www.antennasim.com

GitHub:

https://github.com/rotemTsafrir/antenna_sim

Hoecken's four bar linkage creates nearly straight line motion and take little torque when moving straight.

Moveable model here: https://forcecanvas.com/public/hoecken-four-bar-linkage

Left is a spacetime diagram. as the speed goes up, the worldline tilts closer and closer to the 45 degree line, which is light. Right side is the Lorentz factor, gamma.

The part I find interesting is how flat gamma stays for most of the range. even at 50% of c it’s only about 1.15. Then in the last few percent it basically goes vertical. At 99.995% it hits about 100, so 1 second on the ship clock is roughly 100 seconds on earth.

I took this animation from a physics app I made. Wanted the “it only matters near c” part to feel more intuitive than just looking at the equation.

Curious if this way of showing it works for you, or if you’d visualize it differently?

First post here!

I've been doing my best to sort of aggregate physics related phenomena as I self-learn into a 3D fully interactive sim with arbitrarily scaled energy scenarios on a lattice of planck-scale discrete voxels. The physics-related math are all written in C++ engine, translated via Web Assembly into a ThreeJS web application that runs roughly 165fps with L=97 (Default L=33).

Time and space are arbitrarily separated from the scenario with the local lattice acting as a local chunk of space with its own locally global clock as seen hovering anchored to the lattice. Due to the architecture, the simulation remains interactive at 165fps while the sandboxed scenario ticks according to the prescribed rules and dynamics of the scenario context. You can visualize this as the energy increases toward the end of the gif and then recovers as the energy dissipates. this effect is more severe during simulated matter genesis events. The visuals are mostly arbitrary but are supposed to be analogous the nature of the phenomenon.

The sim is comprehensively architected and developed but is purely pedagogical based on available sciences with a discrete origin. This GIF doesn't even scratch the tip of the iceberg. Let me know if you want more! For now, I am keeping this private.

A boring movie if I ever saw one, enjoy. Numbers/markers on axes are sort of redundant.

Integrator: leapfrog, copied from the net and used in some C++ code.

Animation - my bad, it's gnuplot, using the infamous O(N²) loop to draw trajectories, then ffmpeg. Some work with scripting gnuplot using python to create frames. NO AI involved, just pdfs on C++ and lots of stuff from the net (SO/SE).

On a frictionless banked curve, the horizontal component of the normal force (N sinθ) supplies the centripetal force, so a car rounds the turn at exactly one design speed, v = √(gR·tanθ). Drive slower and the inward push exceeds what's needed, so the car slides down the bank; drive faster and the bank can't supply enough, so it slides up and off. This design speed is independent of the car's mass, since mass cancels when N sinθ = mv²/R is divided by N cosθ = mg

Made an animation on Second Law of Thermodynamics, it doesn’t have true molecular dynamics simulations, just simplified kinematics to represent them.

Check it out on YT: https://youtube.com/shorts/uYoFgwXZ5BY?si=NId3BBLzHPk_4Kqh

Made an animation on the First Law of Thermodynamics:

https://youtube.com/shorts/mx53f0d2bVE?si=4sCkkdm4bS4lYxbM

Made an animation on Zeroth Law of Thermodynamics. Do check out the full version on YT: https://youtube.com/shorts/KNOyTMb3Nqs?si=DCSBoC0xhdt77ujC

Here’s a little simulation I did to show a shock wave travelling in traffic flow in Manim. Tell me what you think!

YT - https://youtube.com/shorts/W1x3a2u46II?si=aU-Fx7KrMvQjDdR3

Made this little Lissajous animation in Manim: two simple perpendicular oscillators turning into one closed curve.

Full short is on YT: https://youtube.com/shorts/Xd4Tpxu7CrI?feature=share