Recent content by mwspice

Partially curiosity. I got the idea from something else I was working on. I was thinking about if there was a varying frictional force between surfaces, and there was a function giving the force at any point of contact, if the force could be modeled as a sum of the forces at each point of contact.

Do you know of any references I could find to help with this?

I think I understand what you are saying, but I'm not sure if it makes sense when I think of the physical system. For example, if we simplify the problem to one dimension and assign a constant value to the force, ##F=1##, we could think of a line with length ##0.5## units, then the integral...

It is both real valued and continuous, and yes, my interval is a rectangle. I basically have a varying force, which depends on the position (x, y), and I want to find the sum of the forces at each point to find a total force. I don't think an integral would work because I don't want to multiply...

Essentially, I have a function of two variables f(x, y), and I want to find the total value (sum) of that function for all values of (x, y) over an interval. How would I do that? The closest thing I can think of is the mean value theorem for integrals, but I want the total value, not the average...

Thanks, I will try that! I thought about saying that they were 0, but I wasn't sure if that was actually the case since they do have a dependence on each other.

Thanks for the reply! I think I understand where you're coming from; however, I don't follow why you say that ## x ## is not given as a function of ## \dot x ## and ## t ## because the way I see it, the integral given above is a function of ## \dot x ## and ## t ## Also, the partial derivative...

Hi, I'm a little confused about something. I have an object, and I want to take the partial derivative of its position wrt velocity and vice versa. I'm not sure how to begin solving this problem. Essentially, what I have is this: ## \frac{\partial x}{\partial \dot x} ## and ## \frac{\partial...

Thank you for your reply! So what is the best way to solve the resulting system of equations? Is it best to just try to use a software like MATLAB to find numerical solutions, or is there a good method for decoupling and solving the equations? If you could point me towards any good resources for...

Hi, I'm currently trying to learn about finding equations of motion from the Lagrange equation, and I'm a little confused about how it applies to multiple degree of freedom systems. I am using the following form of the equation with T as total kinetic energy, V as total potential energy, R as...

I am a new member. I'm studying Mechanical Engineering at Virginia Tech, and I look forward to sharing my learning experience with you all! :)