Exact Equations of Motion for a Deformable Body.
Abstract
The exact equations of motion for an arbitrary deformable body undergoing large deformation are presented in two forms. One of the forms is a momentum formulation and the other is a velocity formulation. Both forms of the equations of motion are derived by vectorial methods, but the resulting equations are shown to be the same as those obtained from a Hamiltonian or Lagrangian formulation. The generality of the final equations is due in part to modeling the deformable body as N particles and separating the degrees of freedom into 6 external or rigid body and into n < or = 3N - 6 internal or deformation degrees of freedom. The internal or deformation degrees of freedom are represented by n generalized coordinates. There is no assumption that these internal or deformation coordinates are small or that their time derivatives are small. The final equations of motion are indendent of the material properties of the body under consideration. In order to make specific use of these equations, specific constitutive equations must be postulated. The most typical constitutive equations used in the spacecraft dynamics literature is to consider the deformable body to consist of a collection of hinged rigid or linearly elastic sub-bodies; then the deformation within one of these sub-bodies is small, but the deformation between the sub-bodies may be arbitrarily large.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 29, 1977
- Accession Number
- ADA042550
Entities
People
- W. Jerkovsky
Organizations
- The Aerospace Corporation