Recent content by KingBongo

mfb: Thank you for your help in particular. It seems like you have an amazing insight into physics and mathematics. Me myself, I was just using brute force here, :)

Ok, I think I got it! Here is the result: Given a fixed maximal length L = z_u-z_l of the sought solid the solution that minimizes J(\Omega) subject to the constraint W(\Omega)=C is a solid cylinder with its center-line parallel to the z-axis, center at (x_c, 0, z_c), length L, and radius...

SteamKing: Yes, but I love math too so I cannot resist doing this, :) Further progress! I have been calculating like crazy yesterday and this is what I have been able to find out. It seems like the optimal solution is a solid cylinder of length L = z_u-z_l with its center-line parallel to the...

bolbteppa: I am glad you asked! Well, it's all about balancing crankshafts for combustion engines :) It's amazing how often I run into mathematical problems when trying to do things in practice. I am probably thinking a bit too much at times.

mfb: Thank you! You provided an example for the case when there are no bounds on the domain of integration in any direction. Then it turns out that the lower bound on I_z is zero. I actually have found such examples myself, namely a cylindrical wedge, i.e. "a piece from a round cake". BUT, what...

Minimizing the Moment of Inertia while keeping the Moment constant Hi there. I am dealing with a mathematical problem which seems to be much harder than I initially expected: Minimize the functional J(\Omega) = \frac{1}{\rho} I_{z} = \int \!\! \int \!\! \int_\Omega \left( x^{2} + y^{2}...

jambaugh: I thought I had simplified it so much it would be pretty easy to handle, :) But no.

Thank you guys. This problem seems to be more involved than I thought. I understand it is a one-dimensional PDE, but the problem is how to model it adequately and to get the initial and boundary conditions right. I am pretty skilled with ODE's, but PDE's are MUCH harder, :( Even setting up the...

Hi. Just for illustration purposes I am trying to model the temperature in the walls of a hollow sphere. The purpose is to (very crudly) approximate the heating effects of a combustion process (running engine). It is assumed that there is gas inside of the sphere. Assumptions: A. Inner and...

genghiskron: Thank you! Well, I am actually not a student. I am a Doctor in control engineering. But this flowing liquidsthing is killing me. No wonder, since I only took a basic course like forever ago, :) Is it thermodynamics we are talking about here? Are there any good books I could read...

I have been thinking about this a lot. It is about conservation of energy. A simplified analysis using Bernoulli's Principle for one-dimensional incompressible liquid fluids should be good enough to gain some understanding (at least for me). Let us also neglect gravitational effects. Assume...

This can't be happening. Doesn't anyone have the slightest clue? I thought this would be an easy problem, :)

I am working on a mechanical model for a Snowmobile and trying to figure out what the differential equations becomes when you have a CVT (Continuous Variable Transmission) instead of a Gear Box. Assume that you have two shafts connected with each another through a (lossless) and stiff gear box...

I have some more; Suppose that you showed what the optimum solution must look like, if it exists, but cannot fulfill the boundary conditions. Does it mean that there does not exist any optimal solution then? How to resolve it? One example: Suppose that you have showed that part of a sphere...

THANK YOU GUYS! For days I have been working hard to prove that a sphere has the smallest surface area, volume fixed, of all solids. I ended up with something that looked like a curvature in 3 dimensions, and that something had to be constant! I wasn't able to show that it represented some kind...