[camacazio]

Well as far as my equations go I didn't bother to go very in depth with the derivations. My equations start from simply the equation for length contraction (Proper length divided by gamma), and using an equation for linear accelleration for my v term in gamma. As for mass, that is not an issue in this case. I'm only dealing with length contraction, not with any sort of relativistic momentum-energy of any system. As a matter of convention, relativistic mass is a term I prefer to avoid. In my most recent special relativity class, our professor made a point of saying how some use relativistic mass, some don't. I like avoiding the term because all equations with mass in relativity involve the rest mass, a factor of gamma, and another factor. Rest mass stays the same for a particle. It's gamma times the other factor that is changing relativistically with this mindset. What changes from different values of energy and momentum is the mass of the system, but that is still different from relativistic mass. It's all the same math in the end, just how I prefer to think about it.

If I had a better way to type out my equations I would do just that. I'll try anyway though. When something is travelling at a velocity near the speed of light with respect to our reference frame, we will see it contract in the direction of motion. The equation for this is L/gamma, where L is the proper length. Proper length is the length of the object at rest. Gamma = 1/sqrt(1-v^2/c^2). This is always a number great than one, and at velocities much below .1 times the speed of light comes out to nearly 1--for this equation, that gives proper length. For my v, I used (in this case, and with my previous letter defintions) v(t)=v-ngt, ng being the coefficient of friction. Realistically something going near the speed of light would take forever to slow down reasonably by friction, but it gave some simple equations for a case when something would slow down. I could use simply a for some constant of accelleration. What's important is the accelleration is linear to avoid a third derivative of anything. So once this constant accelleration is applied opposing the motion, such as friction, the object slows down at a constant rate. Thus, it will expand at some rate. That's what my first derivative represents. It really has no use that I can think of though.