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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

1082.0. "Duffing's Equations" by FORTY2::WHITING (His Nibs) Thu May 11 1989 19:44

I wonder if anybody out there can tell me anything about Duffing's equations
and what's so special about them. I need to work with them very soon and would
like a bit of background first.

                                         Joe

         
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1082.1a couple pointers to tryCTCADM::ROTHIf you plant ice you'll harvest windWed May 17 1989 10:1124
    I only know a little - Duffings equation is a nonlinear second order
    equation with a sinusoidal forcing function; Duffing wrote a monograph
    on this at the turn of the century.  It can be written as a pair of
    coupled equations - this may be why you refered to them as plaural.

    Very little is really known about the solutions - as is usual for
    nonlinear equations, but there are some of the usual tricks - like
    perturbing a linear equation and so on.  You may want to look at the
    following books, and then just do some numerical experiments...

    Try

	Introduction to Nonlinear Differential and Integral Equations
	H. T. Davis, Dover

	Nonlinear Oscillations
	P. Hagedorn, Oxford

    Both are mathematical and have a reasonable discussion of Duffings
    and other equations.  Davis' book in particular has a lot of interesting
    material that is hard to find - use of elliptic functions, asymptotic
    expansions, and so forth.

    - Jim
1082.2Cheers !!FORTY2::WHITINGHey Fatz, you're no Dork !!Wed Jun 28 1989 12:186
    
    Thanks for the pointers Mush, I'll give them a go.
    
                                          joe