Pendulum Snake: Motion of Six Linked Pendulums

This example demonstrates how a chain of six linked pendulums evolves in time, producing a distinctive “snake-like” motion and the corresponding connected geometric trajectory of the joints/endpoints. The main mathematical ideas are angle parameterization (θ values across time), trigonometric relationships implied by the pendulum geometry, and visualization via successive geometric constructions. Construction highlights: it uses Intersect to compute joint/constraint intersection points, Rotate to swing each rod by its corresponding angle θ_i into the new configuration, and Segment to draw each pendulum bar; Max and Angle are used to determine key angle-related quantities. The model is built from objects such as pendulum lengths l1–l6, initial angle θ0, time parameter t, the sequence of angles θ1–θ6, and intermediate points like A and P10–P60 to locate each segment’s endpoint. Suitable for high-school to early university audiences for learning trigonometry-based modeling, parametric animation, and geometric construction techniques.