Another form of equations of motion for constrained multibody systems

Abstract

This paper presents a new and simplified set of explicit equations of motion for constrained mechanical systems. The equations are applicable with both holonomic and nonholonomic systems and the constraints may, or may not, be ideal. It is shown that this set of equations is equivalent to governing equations developed earlier by others. The connection of these equations with Kane's equations is discussed. It is shown that the developed equations are directly applicable with controlled systems where the controlling forces and moments may be subject to constraints. Finally, a procedure is presented for determining which control force systems are equivalent. Examples are presented to demonstrate the advantages, features, and range of application of the equations.

Kinetic quasi-velocities in unilaterally constrained Lagrangian mechanics with impacts and friction

“…u β =q norm n q ) or if the constraints are mutually orthogonal in the kinetic metric so that the matrix (∇h T (q)M −1 (q)∇h(q)) −1 is diagonal. Similar arguments and projectors are used in [13,65,66]; see also [58]. Actually these papers consider orthogonal (in the kinetic metric) projections onto the co-dimension m constrained manifold, whereas we rather consider projections on each vector of the basis (n q , t q ).…”

Explicit equations of motion for U-K equations and its associated deformations in constrained multibody systems

“…The development of the previous explicit dynamics is completed in the form of the first approach, and reference [7] derives new explicit dynamic equations based on the second method. The established equations can be directly applied to a class of constrained control systems.…”

“…In this reduction, local coordinate space was established, and the constrained force and acceleration were decomposed into this local space to obtain a smaller calculation matrix. Liu and Huston (2008) [7] proposed a simpler approach without using generalized inverses.…”

Development of an Efficient Formulation for Volterra’s Equations of Motion for Multibody Dynamical Systems

“…The differentialalgebraic equations governing a dynamical system contain two parts: the ODEs, which are the structural subsystem description, and the algebraic equations, which are the system's constraint equations. The constraints of a mechanical system are usually in a non-integrable velocity form, but many methods consider these equations in acceleration form [26]. That is, almost all traditional methods use constraint equations as a set of second-order equations along with second-order ODEs that are based on generalized coordinates and generalized velocities as motion variables.…”