4569846498

2
Kinematics and dynamics of rigid bodies
2.1 Introduction
The application of a modern multibody systems computer program requires
a good understanding of the underlying theory involved in the formulation
and solution of the equations of motion. Due to the three-dimensional nature
of the problem the theory is best described using vector algebra. In this
chapter the starting point will be the basic definition of a vector and an
explanation of the notation that will be used throughout this text. The vector
theory will be developed to demonstrate, using examples based on suspension
systems, the calculation of new geometry and changes in body orientation,
such as the steer change in a road wheel during vertical motion relative
to the vehicle body. This will be extended to show how velocities and accelerations
may be determined throughout a linked three-dimensional system
of rigid bodies. The definition of forces and moments will lead through to
the definition of the full dynamic formulations typically used in a multibody
systems analysis code.
2.2 Theory of vectors
2.2.1 Position and relative position vectors
Consider the initial definition of the position vector that defines the location
of point P in Figure 2.1.
In this case the vector that defines the position of P relative to the reference
frame O 1 may be completely described in terms of its components with
magnitude Px, Py and Pz. The directions of the components are defined by
Z 1
P
{R P } 1/1
Pz
Y 1
O 1
X 1
Fig. 2.1
Position vector
Py
Px