Physics 310 Classical Mechanics Spring 2000-Ijiri
Handout 3: Equations of motion for simple systems
Many of the problems of interest for this class involve finding the equations of motion.
Force approaches:
In solving for the equations of motion, you can often make progress by considering the
functional dependence of the forces.
Is F zero? --then, a is zero, v is constant, r = vt + const.
Is F a constant? --then, a is a constant a = F/m, just like problems with gravity.
If F varies, what does it depend on? time t? velocity v? position r or in one direction x?
In this case, consider if any of the different representations below make more sense in
light of the functional dependence of the forces:
dx
dv
mv
dt
xd
m
dt
dv
m
dt
pd
F
=
=
=
=
2
2
Note that these may not all be relevant or necessarily true depending on the particular
system in question! (Consider for instance problems with varying mass…)
Energy approaches:
An alternative approach is to recall conservation theorems, and consider the system
energy. For the case of a conservative force (F= - U∇) and potentials U with no explicit
time dependence, the total energy E is a constant. Here, you might use
E= kinetic + potential energy, and solve for x(t) from it.
This should remind you of physics courses past--PHYS 110 of course, but also recall how
in 111, sometimes you considered the electric field (E=F/q) and other the electric
potential (φ or V = U/q).
Starting in Chapter 6, we will begin to consider other approaches (namely Lagrangian or
Hamiltonian ones.)
