Deterministic Reconstruction of Tennis Serve Mechanics: From Aerodynamic Constraints to Internal Torques via Rigid-Body Dynamics

Most conventional studies on tennis serve biomechanics rely on phenomenological observations comparing professional and amateur players or, more recently, on AI-driven statistical analyses of motion data. While effective at describing \textit{what} elite players do, these approaches often fail to explain \textit{why} such motions are physically necessary from a mechanistic perspective. This paper proposes a deterministic, physics-based approach to the tennis serve using a 12-degree-of-freedom multi-segment model of the human upper body. Rather than fitting the model to motion capture data, we solve the inverse kinematics problem via trajectory optimization to rigorously satisfy the aerodynamic boundary conditions required for Flat, Slice, and Kick serves. We subsequently perform an inverse dynamics analysis based on the Principle of Virtual Power to compute the net joint torques. The simulation results reveal that while the kinematic trajectories for different serves may share visual similarities, the underlying kinetic profiles differ drastically. A critical finding is that joints exhibiting minimal angular displacement (kinematically ``quiet'' phases), particularly at the wrist, require substantial and highly time-varying torques to counteract gravitational loading and dynamic coupling effects. By elucidating the dissociation between visible kinematics and internal kinetics, this study provides a first-principles framework for understanding the mechanics of the tennis serve, moving beyond simple imitation of elite techniques.