Dot Physics

A note about numerical calculations

[In a previous post, I talked about numerical calculations](http://scienceblogs.com/dotphysics/2008/10/basics-numerical-calculations/). The basic idea is to use the momentum principle and the following “recipe”:

  • Update the position of the particle
  • Update the momentum of the particle
  • Update the force on the particle

Looks great, right? Well, it mostly is great. I want to give a couple of pointers about the last step, update the force on the particle. How and when can you do this? Really, in numerical calculations, you will see two types of forces:

  • Forces that you can calculate: That looks strange, but it’s true. Maybe you are thinking, can’t you calculate all the forces? – the answer is no. Yes, you can calculate the gravitational force and the electromagnetic force. Also, really all forces you are likely to see are one of those two. You can also calculate the force due to a spring(depends on position), the air resistance force (depends on velocity). These types of forces work well in the above numerical recipe.
  • Forces that you CAN NOT calculate: These are all the other forces. Typically, these are forces of constraint. Suppose a block slides down a plane. Yes, you can calculate the force the plane exerts on the block, but it depends on things other than just the position of the block. The force the plane exerts on the block is such as to keep the block on the plane. You can not calculate this in the same way as the previous category of forces. Yes, technically the force the plane exerts on the block IS the electromagnetic force. If you want to calculate this force between all the atoms in the two objects, I encourage that.

So what does this all mean? This means that you can not use the above “recipe” for whatever you want. Sorry.

(I have a trick I will show you later)