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Strict Modes Everywhere - Bringing Order Into Dynamics of Mechanical Systems by a Potential Compatible With the Geodesic Flow

arXiv · AI, language, vision and robotics · article · Sep 4, 2026 · UTC

Strict nonlinear normal modes provide very regular families of oscillations within conservative mechanical systems. However, a strict normal mode will generally be an isolated curve within the configuration space of the system. In this letter, we design a potential that will densely fill the configuration space with strict normal modes such that each configuration belongs to one mode and each mode passes through a common point, the equilibrium. As the potential can be realized by (nonlinear) elastic elements it can be used to execute a variety of periodic trajectories very efficiently. Most of

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