## Geometry and definitions in the textbook

A body occupies a region Ω in space. The position of an infinitesimal mass element d*m* 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

_{Ω}vd

*m*,

*angular momentum*with respect to an arbitrary point A is defined as

_{A}≡ ∫

_{Ω}r × vd

*m*,

### Postulates

*Euler's laws* postulate that the motion of a body is governed by the force sum ΣF and the moment sum ΣM_{D} with respect to a space-fixed point D acting on the body:

*t*

_{D}= dH

_{D}/d

*t*.

## Pedagogical considerations

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.