Recent content by peterbone

maybe I don't understand what you mean but the software Mathematica is a system for operating on equations and solving them. it can simplify equations so it must have a set of rules for doing so. If you're talking about a new mathematical method for solving problems then no.

g is the acceleration experienced at the surface of the earth. That's how it's defined.

I had exactly the same problem when trying to simulate a double inverted pendulum a few months ago. The system is 3 coupled second order differential equations which I reduced to 6 first order differential equations. Here's the program (written in Delphi)...

I found this web page comparing various methods: http://ceee.rice.edu/Books/CS/chapter5/cost6.html I see what you mean about Cramer's method lurflurf.

There are lots of different methods. For example, numerically. Here is an analytical method I wrote using Cramer's rule to invert the matrix. Delphi source code included. http://www.geocities.com/peterbone3/LinearEquations.zip I assume you're familiar with the matrix representation of a set of...

oh right, it's just the offset then. Yeah, I was thinking that that equation has got a lot of slow routines in it like sins, cosines and square roots. I may try it though.

Thanks, using that equation for the length should speed it up a bit but what is ||S|| ?

Wow, I really appreciate all the effort you put into this. I wasn't sure anyone was going to reply. I understand some of what you've written but having learned mathematics in an engineering degree my knowledge of pure maths and standard notation is limited. The short answer at the end was very...

hello I'm writing a program that uses a quadratic bezier curve and I want it to stay the same length as the curve bends - as the difference in angle between the first and second line segments changes. Here is a program that demonstrates what I'm trying to do...

Thankyou, that was helpful. I also found this site which explains the whole process of simulating a single inverted pendulum and includes the reduction stage. http://drewk.net/projects/ipendulum/ipendulum.html I should be able to use the same method for the double inverted pendulum.

Thanks, but I don't know how to go about reducing the order of coupled differential equations because the 3 unkown variables x, theta1 and theta2 all appear in the same equations.

Hello. First post here. I'm trying to write a program (from scratch) to simulate a double inverted pendulum (a cart with 2 pendulums one on top of the other). The system is modeled with a system of 3 second order ODE's, which I need to solve numerically using Runge Kutta. I know how to solve...