Geometry and definitions in the textbook
A body occupies a region Ω in space. The position of an infinitesimal mass element dm of the body is defined by the position vector r, and the velocity of this mass element is v.
The momentum of a body Ω is defined as
Euler's laws postulate that the motion of a body is governed by the force sum ΣF and the moment sum ΣMD with respect to a space-fixed point D acting on the body:
Although Statics, Particle dynamics and Rigid body dynamics emerge as special cases of Euler's laws for deformable bodies in general motion, it is the belief of the author that it would be a pedagogical mistake to start from the general theoretical framework in a first course of Engineering Mechanics. Introducing Statics first gives students a chance to develop theoretical skills in mathematical inference, vector algebra and the concept of the free-body diagram.