math question

[jasonp]

I'm sorry if this is a dumb question, but I'm having a lot of trouble solving this:

m*a*v+alpha*m*v+beta*v^3-p=0

where m,alpha, beta are constants and

a is the second derivative of x

v is the first derivative of x

also, zero initial conditions.

I have MATLAB if it has to be done numerically.

 

[pelaw]

You are dealing with Nonlinear Second Order differential equation. It is no surprise that you are having difficulty finding a solution. Go to google books and research nonlinear second order DE, and you will quickly realize the problem. The best advice I can give you is get an expert in DE. Write to your school's math department to tell you more, or if you get lucky on some math forum you may get an answer on how to qualitatively or numerically assess possible solutions, but certainly not a general solutions.

http://docs.google.com/viewer?a=v&q=ca...irsaLlPn8LRZbvw

 

[benbo]

I agree with pelaw - I wouldn't know where to start.

Generally, when they solve these things, I think they make substitutions to convert it to an ODE or a couple ODEs, and then try to get something separable. But this looks exceptionally complicated especially since the first term has the first differential multiplied by the second differential. And you have to apply the chain rule up the ying yang. Not to mention the cube of the first differential in the last term.

Where did this equation arise? Is this some sort of boundary value problem? You could check to see if this is a known equation.

Otherwise, you probably need to solve it numerically, in which case I wouldn't know where to begin either. It's been about 25 years since I even saw anything like this. I never saw it in EE school, only when I was studying physics.

I am intrerested to see if you find out how to do it and I am overlooking or overcomplicating something.

 

[Riceman]

reduce it to a system of first order ODE with initial conditions. then solve them using Runge Kutta degree four algorithm. I have no idea what this equation represents, maybe some complicated wave equations, or circuits. If you really want I can probably find the algorithm from my numerical analysis class, but they should have a pseudo code for it in your text book.

 

[benbo]

^^^

Riceman,

I hope you stick with engineering and can find a good paying interesting job. No offense to orthodontists, but you seem too smart to spend all day twisting wires on kid's teeth.

 

[Dleg]

LOL! I'm with benbo. I wouldn't even know where to begin with that. You can't be wasting that talent on teeth.

 

[RIP - VTEnviro]

^^^Riceman,

I hope you stick with engineering and can find a good paying interesting job. No offense to orthodontists, but you seem too smart to spend all day twisting wires on kid's teeth.

 

[ironman]

I would strongly suggest taking a course called advanced engineering math, you go into second and even third order nonlinear DE, Fourier transforms, partial differential equations and conformal mapping, the class was brutal and took me about 20 hrs a week out side of class to do well in but was worth it, you also want to watch out for seemingly simple first order DE that involve division that turn out to be bernouli DE's not insurmountable but it threw me for a loop one time. Even after just the summer I could not do it off the top of my head I would have to refer back to my notes and mathcad templates I developed in the class. I would also suggest taking a PDE course, all of these courses also count for you CEU credits. It is kind of nice keeping up on your math, I was able to do a settle out pressure calc from scratch and even used an integral on the back of a napkin so to speak (not acutally a napkin but scratch paper). I would like to be able to derive valve opening and water hammer equations from scratch as well that would be cool.

The real brutal head achs are in PDE's, but unless you are doing PhD level research you should never encounter a PDE in engineering practice, other than maybe the simplest of PDE's that have well established solution methods even then I have never seen a PDE in engineering pracitce. I am actually taking a 300 level E&M course this semester and spring so I can start doing a MS in EE (antenna theory, wave optics, etc)