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Help with nonlinear differential equation?
From the simple problem of picking up a chain subject to gravity with a constant force, the equation of motion looks like:
(a - bL) = L(L''), where a and b are constants.
Is this solvable for L(t)?
1 Answer
- xyzzyLv 76 years agoFavorite Answer
v = dL/dt
dv/dt = dv/dL dL/dt = dv/dL v = L ''
(a - bL) = L dv/dL v
a/L - b dL =v dv
a ln L - bL + c = 1/2 v^2
(2 a ln L + 2b L + c)^1/2 = v
(2 a ln L + 2b L + c)^1/2 = dL /dt
dt = (2 a ln L + 2b L + c)^-1/2 dL
and now I am stuck.