Space Elevator Climber-Induced Tether Resonance

A space elevator's ribbon-like tether is not perfectly rigid — it is a taut string thousands of kilometres long, and a climbing vehicle crawling up it injects small lateral kicks through its roller drive that can excite real transverse waves. This simulator solves the 1-D wave equation for a tether with a physically motivated tension profile (rising toward geostationary altitude, falling toward the counterweight, so wave speed varies with position), driven by a moving point force representing the climber. Tune the climber's speed and its vibration amplitude/frequency against the tether's damping to see traveling waves reflect off the fixed anchor and counterweight and, when the forcing period lines up with the tether's round-trip wave-travel time, build into resonant standing-wave sway — the same coupling that real climber speed-profiles are designed to avoid.