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Integration of Newton’s
Equation of Motion
3.1 INTRODUCTION
In Chapter 2, we saw that Newton’s second law can be written as
d
d
P
t
F=
,
where
is the momentum of the particle, and
is the external applied force. When the mass m is
constant, we can write it as a second-order differential equation:
m
r
t
F
d
d
2
2
=
and it is called the equation of motion of the particle. When the force
is known, the equation of
motion becomes a second-order differential equation for the unknown function r(t), the path or
orbit of the particle. The objective of this chapter is to seek solutions to this equation of motion for
var ...