The equation of motion for a pendulum is y''=-(g/L)sin(y), where y represents the angle of the stiff rod with respect to the vertical, g is the acceleration of gravity, L is the length of the rod. y also varies with respect to time. I've seen how this particular equation is derived, but I would like to know more about the general problem of modeling mechanical systems with constraints. Does anyone have some insight to offer? How could I view this problem from the mechanical perspective (finding positions, energies, momentums, etc.).

One of the tricks is to set up your coordinate system to coincide with the constraint. The pendulum problem is solved by using spherical coordinates in 2-D; because r is fixed, the only variable is now the angle. That simplifies the problem. I imagine engineering texts do this a lot more than physics.

It's not always as simple as a pendulum, though. How could I analyze a more complicated constraint?

 

An example I can think of is motion along a fixed path under the influence of 3 charges (kind of like the 3-body problem).

Is there a general method that could work for analyzing all sorts of constraints?

It's not always as simple as a pendulum, though. How could I analyze a more complicated constraint?

 

An example I can think of is motion along a fixed path under the influence of 3 charges (kind of like the 3-body problem).

Is there a general method that could work for analyzing all sorts of constraints?

 

Look at Lagrangian and Hamiltonian mechanics in any book with a title like "Classical Mechanics" or Classical Dynamics". The books by Goldstein or Marion would do nicely.