Translational Dynamics

We studied first geometry, then kinematics, and now have amassed enough equipage to investigate dynamics, the effect of force on mass. In this chapter we concentrate on the motions of the center of mass (c. m.), assuming that all mass of a vehicle is localized at that point. The c. m., subjected to forces, describes trajectories in space, as recorded by an observer. Later in Chapter 6 we will model the vehicle as a body and watch it rotate under externally applied moments. Both combined, translation and attitude, convey the full six degrees of freedom of vehicle motions.

The physical law that governs translational motions is Newton’s second law. After 300 years it still has maintained its preeminence in trajectory simulations. Most useful for engineering applications is the formulation: the time rate of change of linear momentum equals the applied external force. Therefore, before we treat Newton’s law in detail we discuss the linear momentum of single and clustered bodies. Then, after deriving the translational equations of motions from Newton’s law we discuss two transformations resulting from changes of reference frame and reference point and conclude the chapter with examples motivated by applications.