Learning Visualizations
Interactive 3D explorations of mathematical concepts
Linear Algebra
Dot Product
Vectors, angles, and projection
Cross Product
Perpendicular vectors and parallelogram area
Moment of a Force
Torque as a cross product: M = r × F
Kinematics
Angular Velocity
Why ω is orthogonal, and v = ω × r
Plane Motion
Radial and transverse components in polar coordinates
Instantaneous Center
The point about which the body is rotating instantaneously
Euler Angles
ψ, θ, φ and transformation of displacements
Areal Rate
r × v, equal areas, and Kepler's second law
Circular Motion
v = rω, centripetal and tangential acceleration
Particle Dynamics
Impulse & Momentum Visualisation
Visualisation of impulse and momentum.
Gyrodynamics
Polhode & Herpolhode
The motion of the instantaneous rotation axis in body and space frames.