The Lagrangian Derivation of Kane's Equations
نویسنده
چکیده
The Lagrangian approach to the development of dynamics equations for a multi-body system, constrained or otherwise, requires solving the forWard kinematics of the system at velocity level in order to derive the kinetic energy of the system. The kinetic-energy expression should then be differentiated multiple times to derive the equations of motion of the system. Among these differentiations, the partial derivative of kinetic energy with respect to the system generalized coordinates is specially cumbersome. In this paper, we will derive this partial derivative using a novel kinematic relation for the partial derivative of angular velocity with respect to the system generalized coordinates. It will be shown that, as a result of the use of this relation, the equations of motion of the system are directly derived in the form of Kane's equations.
منابع مشابه
Development and Application of an ALE Large Deformation Formulation
This paper presents a complete derivation and implementation of the Arbitrary Lagrangian Eulerian (ALE) formulation for the simulation of nonlinear static and dynamic problems in solid mechanics. While most of the previous work done on ALE for dynamic applications was mainly based on operator split and explicit calculations, this work derives the quasi-static and dynamic ALE equations in its si...
متن کاملDynamics of Flexible Manipulators
This paper presents an application of Continuum (i.e. Lagrangian) and Finite Element Techniques to flexible manipulator arms for derivation of the corresponding Dynamic Equations of Motion. Specifically a one-link flexible arm is considered for detailed analysis, and the results are extended for the case of a two - link flexible manipulator. Numerical examples are given for the case of both one...
متن کاملLagrangian Averaging for Compressible Fluids
This paper extends the derivation of the Lagrangian averaged Euler (LAEα) equations to the case of barotropic compressible flows. The aim of Lagrangian averaging is to regularize the compressible Euler equations by adding dispersion instead of artificial viscosity. Along the way, the derivation of the isotropic and anisotropic LAE-α equations is simplified and clarified. The derivation in this ...
متن کاملThe Anisotropic Lagrangian Averaged Euler and Navier-Stokes Equations
The purpose of this paper is twofold. First, we give a derivation of the Lagrangian averaged Euler (LAE-α) and Navier-Stokes (LANS-α) equations. This theory involves a spatial scale α and the equations are designed to accurately capture the dynamics of the Euler and Navier-Stokes equations at length scales larger than α, while averaging the motion at scales smaller than α. The derivation involv...
متن کاملLagrangian Averaging, Nonlinear Waves, and Shock Regularization
In this thesis, we explore various models for the flow of a compressible fluid as well as model equations for shock formation, one of the main features of compressible fluid flows. We begin by reviewing the variational structure of compressible fluid mechanics. We derive the barotropic compressible Euler equations from a variational principle in the material frame. The particle relabeling symme...
متن کامل