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coupled second order differential equations

• To: mathgroup at smc.vnet.net
• Subject: [mg2424] coupled second order differential equations
• From: fainberg at gsfc.nasa.gov (Joseph Fainberg)
• Date: Sun, 5 Nov 1995 16:06:40 -0500
• Organization: NASA Goddard Space Flight Center -- Greenbelt, Maryland USA

We have a system of two second order nonlinear ordinary differential
equations of the form:

y'' = f(y,w)
w'' = g(y,w)

where y=y(t), w=w(t) and f and g are nonlinear functions, and '' represents
the second derivative with respect to t.

This system has the appearance of 2 coupled nonlinear oscillators.
Indeed, when we linearize near the equilibrium point, we find two
oscillation modes with different frequencies.

Does anyone know of a reference where this system of second order
differential equations is discussed, particularly with respect to
stability, possible integral of motion (analogous to total energy),
etc?

Thanks,

fainberg at gsfc.nasa.gov