Re: Broken DSolve + Piecewise forcing function
- To: mathgroup at smc.vnet.net
- Subject: [mg59593] Re: [mg59566] Broken DSolve + Piecewise forcing function
- From: Pratik Desai <pdesai1 at umbc.edu>
- Date: Sat, 13 Aug 2005 03:26:22 -0400 (EDT)
- References: <200508120409.AAA11249@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Chris Chiasson wrote: >Dear MathGroup, >Somehow, I have managed to feed DSolve a system of equations to which >it seems to produce an unphysical answer. The problem seems to >originate from the forcing function, which is Piecewise defined. I >have correctly solved the equations with NDSolve. I have also >correctly solved the equations using a Fourier series approximation to >the forcing function and DSolve. All that remains is to figure out >what is going wrong with the Piecewise forcing function and the DSolve >command. >The notebook gives the full problem statement and some explanation on >the origins of the equation system. >http://chrischiasson.com/MathGroup/BrokenDSolvePiecewise.nb >Please help me figure out what is wrong. >Thank you for your time, > > Wow! I just realized how my control class would have been a little easier, if I had known mathematica then There are two things that I see 1. When you put your equation in LTI form would it not be better to put it in State Space form dx/dt=A.x we know the solution to this is x= MatrixExp[A].x(0) Hence you can work around actually solving the equation using DSolve with piecewise forcing functions. Then its just a case of some algebraic manipulation to get x. 2. When you calculate your series solution, may be you can use laplace transform, since both of your components of the series are in t. Atleast that is what I can make out from your code, again I may be completely wrong and making a fool out of myself :-) Hope this helps Pratik Desai -- Pratik Desai Graduate Student UMBC Department of Mechanical Engineering Phone: 410 455 8134
- References:
- Broken DSolve + Piecewise forcing function
- From: Chris Chiasson <chris.chiasson@gmail.com>
- Broken DSolve + Piecewise forcing function