Introduction

So far, we have been discussing about the kinematics and dynamics of a single point particle, where a particle is an idealized material body having its mass concentrated at a point. This idealization enables us to simplify the motion of a particle to a motion of a point in space [1]. By defining a inertial reference frame (Newton’s First Law of motion) with (at most) three bases, Newton’s Second Law of motion provides us (at most) three second-order differential equation.

The idealized point particle served as a great model in classical mechanics — in particular, analyzing the motion of planetary motion. In fact, Newton’s Laws of motion were deduced by analyzing the motion of planets under the gravitational forces of the sun [2]. Such idealization was sufficient for the analysis of planetary motion, since the distance between planets are long enough to neglect the size of the each planet.1

However, the approach becomes cumbersome (or even fails) when the size and the shape of the object itself is not negligible. For instance, consider kinematics and dynamics of a block of aluminium moving in space.2 Considering the size of Avogadro constant, it is immediate that taking account for the dynamics of each particle is almost impossible. Hence, an idealization rather than a point particle is necessary.



Rigid Body Assumption

Fortunately, the rigid body assumption (or idealization) can significantly reduce the complexity of the problem [4]. A rigid body (or object) is a collection of particles that the distances between the particles do not change as the body moves and/or rotates. In other words, a rigid body is an idealized object that do not deform or bend under the influence of external forces. As with an idealized point particle, a rigid body is an idealization, as all materials have some degree of elasticity and deform to some extent when subjected to external forces. Nevertheless, rigid body assumption is a useful simplification for the analysis of the kinematics and dynamics of rigid objects.

[1]
D. T. Greenwood, Classical dynamics. Courier Corporation, 1997, p. 1.
[2]
C. Lanczos, The variational principles of mechanics. Courier Corporation, 2012, pp. 3–4.
[3]
C. Elliott, “The spinning top,” Durham University. Durham, UK, 2009.
[4]
V. Duindam, “Port-based modeling and control for efficient bipedal walking robots,” These de doctorat, University of Twente, 2006.

  1. As George E.P. Box said, all models are wrong, but some are useful.↩︎

  2. Or, one can consider the dynamics of a spinning top, where the resulting motion amazed renowned physicists [3].↩︎