Foucault’s Pendulum: 3D Visualization of Earth-Driven Plane Rotation

This example demonstrates the Foucault pendulum effect: the oscillation plane rotates gradually, with the rotation rate depending on latitude. The construction visualizes how Earth’s rotation changes the pendulum’s plane orientation over time using a 3D geometric and parametric model. Key mathematical ideas include 3D vector representation, rotation (transforming direction vectors), angle relationships, orthogonal planes, and parameter-driven motion that can be interpreted in a differential/kinematic sense. Construction highlights: Sphere models the Earth; Vector, Point, and Segment define the pendulum and direction elements; Circle and Tangent create relevant circular geometry and tangency constraints; UnitVector and Rotate perform the actual rotational updates; OrthogonalPlane builds planes perpendicular to the current direction, while Intersect locates their intersections. Sequence and PolyLine generate a time-stepped direction/trajectory visualization, controlled by animation parameters such as α, t0, t1, dt, tt, and variables for latitude/longitude, direction, velocity, scale, and re/initialization controls. Suitable for advanced high-school STEM demonstrations and early university coursework on geometric construction, vector transformations, and physics-math modeling.