Skip to main content Contents Index Prev Up Next \(\newcommand{\val}{Val\text{00E9}ry}
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Chapter 11 Newton-Euler Formalism
This chapter is devoted to Newton-Euler formulation of principles which govern the motion of rigid bodies. We start by stating the Principle of Virtual Power which is applicable to all material systems. To provide some insight into this principle, we consider the case of systems of particles whose motions are governed by Newton’s second law. In order to eliminate the virtual power of internal forces, we identify a particular class of virtual velocity field. This principle represents the keystone of engineering dynamics, from which all theorems will be derived:
In this chapter, we derive the principal result of vectorial dynamics, the Fundamental Theorem of Dynamics (FTD): it relates the rate of change of linear momentum and angular momentum of a material system to the externally applied forces and moments. After illustrating the use of this theorem on a few examples, we examine the conditions which lead to conservation of linear or angular momentum. We then study special types of motions of rigid bodies: rotational and Euler-Poinsot motions. The latter is known as torque-free rotational motion and is relevant to spacecraft attitude dynamics. We also examine the problem of dynamic balancing of rigid bodies in rotational motion. Finally, we provide guidelines for the solution of multibody problems.
