Movement Equations 3

5Methodological Formulary

The objective of the books in this series is to allow the reader to correctly develop mechanic formalism, despite its apparent complexity. This development wants to set up all the elements which have a part in establishing the movement equations of the mechanical system, the motion of which is under consideration; it calls upon several notions. In spite of the author’s intention towards clarity and their desire to give the readers the capability in succeeding this development, there is danger of confusion for them if they lack knowledge in the subject. This is why it makes sense to provide a methodological guide which gathers the essential formulae to trace the primary steps of the development of mechanic formalism of non-deformable solids.

5.1. Reference outline on the motion of a solid

5.1.1. Representation of a frame

The principle of locating a body in space uses two simultaneous measures:

• – the distance of the body at a given point in space considered as a fixed reference for the examined motion;
• – that of the oriented segment “origin-body” in relation to three distinct directions, neither collinear nor coplanar.

The set that includes the reference point and the three directions forms the reference frame. The three directions are defined by the three independent vectors – neither all coplanar, nor collinear for at least two of them – and are ...