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