2019/11/05 by Albu-Schaeffer, Alin, Dominic Lakatos, Stefano Stramigioli +2
Engineering · Physics and Astronomy · #Control and Dynamics of Mobile Robots #Dynamics and Control of Mechanical Systems #Experimental and Theoretical Physics Studies #FOS: Electrical engineering #Robotic Locomotion and Control #Soil Mechanics and Vehicle Dynamics #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1911.01882
openalex publication_date 2019/11/05 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
For the study of highly nonlinear, conservative dynamic systems, finding\nspecial periodic solutions which can be seen as generalization of the\nwell-known normal modes of linear systems is very attractive. However, the\nstudy of low-dimensional invariant manifolds in the form of nonlinear normal\nmodes is rather a niche topic, treated mainly in the context of structural\nmechanics for systems with Euclidean metrics, i.e., for point masses connected\nby nonlinear springs. Newest results emphasize, however, that a very rich\nstructure of periodic and low-dimensional solutions exist also within nonlinear\nsystems such as elastic multi-body systems encountered in the biomechanics of\nhumans and animals or of humanoid and quadruped robots, which are characterized\nby a non-constant metric tensor. This paper discusses different generalizations\nof linear oscillation modes to nonlinear systems and proposes a definition of\nstrict nonlinear normal modes, which matches most of the relevant properties of\nthe linear modes. The main contributions are a theorem providing necessary and\nsufficient conditions for the existence of strict oscillation modes on systems\nendowed with a Riemannian metric and a potential field as well as a\nconstructive example of designing such modes in the case of an elastic double\npendulum.\n