TABLE OF CONTENTS KEY FEATURES
The key features in this chapter are (i) the vector equation of motion and its reduction to scalar equations, (ii) motion in a force field, (iii) geometrical constraints and forces of con straint, and (iv) linear and quadratic resistance forces.
Particle dynamics is concerned with the problem of calculating the motion of a particle that is acted upon by specified forces. Our starting point is Newton s laws. However, since the First Law merely tells us that we should observe the motion from an inertial frame, and the Third Law will never be used (since there is only one particle), the entirety of particle dynamics is based on the Second Law
where F 1 , F 2 , , F N are the various forces that are acting on the particle. The typical method of solution is to write the Second Law in the form
which is a first order ODE for the unknown velocity function ?( t) and is called the equation of motion of the particle. If the initial value of ? is given, then equation (4.1) can often be solved to yield ? as a function of the time t. Once ? is determined (and if the initial position of the particle is given), the position vector r of the particle at time t can be found by solving the first order ODE d r /dt = ?
