Ruby Tyra
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I'm having some difficulties figuring out how to linearize second order differential equations for a double pendulum.
I have an equation that is in the form of
\theta_{1}''\normalsize = function [\theta_{1},\theta_{2},\theta_{1}',\theta_{2}']
(The original equation is found at http://www.myphysicslab.com/dbl_pendulum.html, the equations inside the orange rectangle.)
I was told to replace that function by a linear function of all four variables but I don't know where to start with that since the original equation is much more complex than the simple pendulum example we were given.
Thank you!
I have an equation that is in the form of
\theta_{1}''\normalsize = function [\theta_{1},\theta_{2},\theta_{1}',\theta_{2}']
(The original equation is found at http://www.myphysicslab.com/dbl_pendulum.html, the equations inside the orange rectangle.)
I was told to replace that function by a linear function of all four variables but I don't know where to start with that since the original equation is much more complex than the simple pendulum example we were given.
Thank you!