Modeling Hybrid Parameter Multiple Body systems: A different approach

Abstract

In this paper, the Hybrid Parameter Multiple Body (HPMB) system modeling problem is addressed. Presented, is a systematic methodology for deriving equations of motion for these highly complex systems. The methodology is founded in variational principles, but uses vector algebra to eliminate tedium. The variational nature of the methodology allows rigorous equation formulation providing not only the complete non-linear, hybrid, differential equations, but also the boundary conditions. One novelty of the method lies in the fact that its variational nature is transparent to the user. This enables it to be effectively used by researchers having a working knowledge of Lagrange's method. The methodology is formulated in the system's constraint-free sub-space of the configuration space, thus all constraints (holonomic and nonholonomic) are automatically satisfied. Since Lagrange multipliers are not needed, the method produces a minimal realization. The spatial dimensions of the continuum bodies are not restricted and the inter-body connections are completely general.