Three-dimensional mapping analysis of a capsule system with bilateral elastic constraints

Abstract

The three-dimensional mapping of the capsule system with bilateral elastic constraints is studied, which is rarely seen in the literature at present. The bilaterally constrained elastic system is suitable for small-scale capsule models. Compared with the unilaterally constrained elastic capsule system, the bilaterally constrained elastic system has a more complex switching mechanism on the boundary, a larger number of local mappings, and a richer whole motion process and bifurcation. The detailed analysis of the bilaterally constrained elastic capsule models can provide more effective theoretical support for the practical application of small-scale capsule models. In this paper, the local dynamics of non-smooth boundaries caused by dry friction and contact and global dynamics in a bilaterally constrained elastic capsule system are analyzed. By considering the vector fields near the boundary surfaces and boundary lines, we get the switching mechanisms on the boundary surfaces and boundary lines and find all possible local mappings. Under the guidance of theoretical analysis, we obtain the sliding bifurcations and boundary-intersection crossing bifurcations by changing the external excitation amplitude. The numerical simulation shows that the bifurcation points and the change of the motion state before and after the bifurcation are consistent with the theoretical results, indicating that this analysis method can be used to accurately discuss the dynamic behaviors of the bilaterally constrained elastic capsule system and mappings can express the dynamic behaviors.