In motion control, the hidden variable that often dominates system behavior isn’t velocity or even acceleration—it’s jerk, the time derivative of acceleration. When a system follows a rectangular velocity profile, it implies instantaneous changes in velocity, which mathematically requires infinite acceleration over zero time. That translates to impulsive forces, effectively infinite jerk, which no physical system can realize. Instead, the result is broadband excitation of structural modes, fluid sloshing, and loss of control authority.
In the liquid payload shown here, the sudden acceleration step introduces a sharp inertial mismatch between the container and the fluid. The fluid resists motion due to its inertia, generating a transient free-surface deformation. This manifests as slosh dynamics governed by gravity waves and container geometry, with energy injected across multiple frequencies. The outcome is chaotic surface motion and eventual spill, not because the velocity is too hig...
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