Transcription of LS.4 Decoupling Systems - MIT Mathematics
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LS.4 Decoupling Systems - MIT Mathematics
Decoupling Systems1. Changing common way of handling mathematical models of scientific orengineering problems isto look for a change of coordinates or a change of variables which simplifies the problem. Wehandled some types of first-order ODE s the Bernouilli equation and the homogeneousequation, for instance by making a change of dependent variable which converted theminto equations we already knew how to solve. Another examplewould be the use of polaror spherical coordinates when a problem has a center of example from physics is the description of the acceleration of a particle moving inthe plane: to get insight into the acceleration vector, a newcoordinate system is introducedwhose basis vectors aretandn(the unit tangent and normal to the motion), with the resultthatF=mabecomes simpler to are going to do something like that here. Starting with a homogeneous linear systemwith constant coefficients, we want to make a linear change of coordinates which simplifiesthe system .
LS.4 Decoupling Systems 1. Changing variables. A common way of handling mathematical models of scientific or engineering problems is to look for a change of coordinates or a change of variables which simplifies the problem.
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