I just tried that with this specific example, and using my 2nd eigen vector ##(-1, 2)## I do indeed get that [M]u = λu. So now I'm just more puzzled. I don't understand why my eigen vector doesn't yield the desired diagonal matrix. I know that you can just assume the diagonalized matrix is just...
Thank you by the way Orodruin for mentioning that it's nonlinear. I'm doing some research on "homogeneous first-order nonlinear ordinary differential equations." I guess that's the kind of equation this is.
I treated ##
\int {\frac {\mathrm {d \dot{x}}} {\mathrm {\dot{x^2}}}}## the same as ##\int \frac {\mathrm{dx}} {x^2} = \int x^{-2} \mathrm{dx} = -x^{-1}##.
So then I got ##- \dot x^{-1} = \frac {\mathrm {dt}}{dx} = \frac {1}{2m}\rho CA t##.
Then multiplied and divided: ##\frac {\mathrm...
Hello all, I want to say thank you in advance for any and all advice on my question. My classical mechanics textbook (Marion Thornton) has been taking me through motion for a particle with retarding forces.
The example it keeps giving is:
m dv/dt = -kmv
which can be solved for:
v = v0e-kt...