Multibody Dynamics Calculator

Calculator Inputs

Responsive input grid: 3 columns on large screens, 2 on smaller, 1 on mobile.

Units are user-defined. Keep them consistent.

Model

Choose the multibody system you want to evaluate.

N-body Settings

Number of bodies (2–6)

Gravitational constant (G)

Use 1 for normalized units, or SI value if desired.

Softening length (eps)

Prevents singular forces at very small separations.

Duration (T)

Time step (dt)

Integration method

Max recorded rows

Controls preview and CSV density via downsampling.

Body Parameters

Set mass, initial position (x,y), and velocity (vx,vy). Only the first N bodies are used.

Body 1

m, x, y, vx, vy

Mass

Body 2

m, x, y, vx, vy

Mass

Body 3

m, x, y, vx, vy

Mass

Body 4

m, x, y, vx, vy

Mass

Body 5

m, x, y, vx, vy

Mass

Body 6

m, x, y, vx, vy

Mass

Reset

Example Data Table

Use these as starting points. Keep units consistent throughout your inputs.

N-body example (normalized units)

Body	m	x	y	vx	vy
1	1	-1	0	0.3	0.1
2	1	1	0	-0.3	0.1
3	1	0	1.5	0	-0.2

Suggested settings: G=1, eps=0.001, T=10, dt=0.01, RK4.

Double pendulum example (SI-like)

m1	m2	L1	L2	g	theta1	theta2
1	1	1	1	9.81	120	60

Suggested settings: omega1=0, omega2=0, T=10, dt=0.01, RK4.

Formula Used

Gravitational N-body (2D)

Each body i accelerates due to all other bodies j.

Relative displacement: r_ij = (x_j - x_i, y_j - y_i)
Softened distance: |r_ij| = sqrt((dx)^2 + (dy)^2 + eps^2)
Acceleration: a_i = Σ_{j≠i} G m_j r_ij / |r_ij|^3
Energy: KE = Σ 1/2 m v^2, PE = -Σ_{i<j} G m_i m_j / |r_ij|

Double Pendulum (planar)

Two coupled rotational degrees of freedom, solved with standard Lagrange-derived equations.

State: (theta1, theta2, omega1, omega2)
Derivatives: dtheta/dt = omega and domega/dt = alpha(theta, omega)
Numerical integration: Semi-implicit Euler or fourth-order Runge-Kutta.
Energy is computed from link endpoint velocities and heights.

Tip: Smaller time steps improve stability, especially for chaotic motion.

How to Use This Calculator

Select a model: N-body gravity or double pendulum.
Enter consistent units for all parameters.
Choose duration, time step, and an integration method.
Provide initial conditions for bodies or angles.
Press Calculate to view results above the form.
Use Download CSV/PDF to export your computed dataset.

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