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For Engineers · Rotational Dynamics

Rotational Dynamics for a hammer throw

Built for engineers using it for real design work. Go from concept to a running model in the browser, then scale to the cloud when needed. Simulate a hammer throw live below — adjust the inputs and watch it respond, right in your browser.

Collisions

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Elastic CollisionsLive

momentum & energy conservation

Controls

Speed1×

Presets

Balls collide with impulse-based physics. At restitution 1, kinetic energy is conserved; below 1, collisions are inelastic and energy drains away.

Balls

Restitution

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Data Inspector

Balls12

Total KE0.00e+0

Collisionselastic

Governing equation

j = \frac{- ( 1 + e ) ( v _{b} - v _{a} ) \cdot n ^}{1/ m _{a} + 1/ m _{b}}, e = 1.00

Reading this result: With restitution 1 every bounce is perfectly elastic, so the total kinetic energy of all 12 balls stays constant forever — a 2D model of an ideal gas.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Double Pendulum

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Double Pendulum StudioLive

chaotic dynamics · RK4

Controls

Speed1×

Tiny changes in the start explode into totally different motion — deterministic chaos. Drag either bob to set a new starting position; it pauses playback automatically.

Presets

Lower bob mass

Gravity g

▶ Run in Python

Data Inspector

IntegratorRK4

SystemChaotic

DOF2

Lower bob mass10

Gravity g9.8

Governing equation

\ddot{θ}_{1} \ddot{θ}_{2} = \frac{- g ( 2 m _{1} + m _{2} ) sin θ _{1} - m _{2} g sin ( θ _{1} - 2 θ _{2} ) - 2 m _{2} sin ( θ _{1} - θ _{2} ) ( θ ˙ _{2}^{2} L _{2} + θ ˙ _{1}^{2} L _{1} cos ( θ _{1} - θ _{2} ) )}{L _{1} ( 2 m _{1} + m _{2} - m _{2} cos ( 2 θ _{1} - 2 θ _{2} ) )} = \frac{2 sin ( θ _{1} - θ _{2} ) ( θ ˙ _{1}^{2} L _{1} ( m _{1} + m _{2} ) + g ( m _{1} + m _{2} ) cos θ _{1} + θ ˙ _{2}^{2} L _{2} m _{2} cos ( θ _{1} - θ _{2} ) )}{L _{2} ( 2 m _{1} + m _{2} - m _{2} cos ( 2 θ _{1} - 2 θ _{2} ) )} m_{1} = 10, m_{2} = 10, L_{1} = L_{2} = 1.2, g = 9.8

Reading this result: Starting both arms at 90° (π/2) with lower-bob mass 10 and g 9.8 puts the pendulum firmly in its chaotic regime. Unlike a small-angle swing, which would be near-periodic, here trajectories that differ by 0.02 rad diverge exponentially — a positive Lyapunov exponent.

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Frequently asked questions

Is this good for engineers?: Yes — this version of "Rotational Dynamics for a hammer throw" is framed for engineers using it for real design work. Go from concept to a running model in the browser, then scale to the cloud when needed.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.