1. Kinematics

Kinematics deals with the motion of mechanical systems, without taking into account the causes of motion.

Classical mechanics relies on the concepts of absolute 3-dimensional Euclidean space, \(E^3\), and absolute time.

Space and time. Briefly, what is space? It’s something you can measure with ruler (for distances) and square (for angles), or other space-measurment devices. Newton mechanics relies on space modeled as Euclidean space, a physical entity where the Euclidean geometry holds. What is time? It’s something you can measure with a clock or other timekeeping devices, that can be related to order of events, and causality (cause comes before consequences).

Models. Different models of physical systems can be derived with an abstraction and modelling process, depending on the characteristics of the system under investigation and on the level of detail required by the analysis.

These models can be classified by:

• dimensions: 0: point; 1: line; 2: surfaces; 3: volume solid

• deformation: deformable or rigid components

A system can be composed of several components, either free or connected with constraints.

Here, the focus goes to the kinematics of points and rigid bodies, while deformable bodies are described in continuous mechanics - kinematics.

While space and time are absolute, the motion of a system is usually the motion relative to an observer or to a reference frame. After treating the kinematics of points and rigid bodies w.r.t. a given reference frame, relative kinematics provides the description of the motion of the same system w.r.t. 2 different observers/reference frames in relative motion.

Definition 1.1 (Configuration)

Definition 1.2 (State)