- #1
keebler71
- 1
- 0
Ok...so this isn't homework (well past that at 39!) but I'm trying to brush off the old cobwebs and solve a vehicle motion problem. Specically, I'm trying to find the
Ok...so this isn't homework (well past that at 39!) but I'm trying to brush off the old cobwebs and solve a vehicle motion dynamics problem. Specifically I’m trying to solve for the velocity history of the vehicle subject to accelerations that vary with the velocity and velocity squared. Eventually I’ll add a forcing term and I’d like to solve this using the Laplace Transform.
Here is a generalized version of the equation:
v’ (t) = k1*v(t)^2 + k2^v(t) + k3
The left side is easy:
L[v’(t)] = sV(s) - v(0)
But I’ve been stumped by the right side. Specifically, I am having trouble finding the L[v(t)^2] term. I’ve tried substituting into the definition of the LT and integrating by parts but not luck so far and can't find an similar example on the web or in a table... Any suggestions?
Homework Statement
Ok...so this isn't homework (well past that at 39!) but I'm trying to brush off the old cobwebs and solve a vehicle motion dynamics problem. Specifically I’m trying to solve for the velocity history of the vehicle subject to accelerations that vary with the velocity and velocity squared. Eventually I’ll add a forcing term and I’d like to solve this using the Laplace Transform.
Homework Equations
Here is a generalized version of the equation:
v’ (t) = k1*v(t)^2 + k2^v(t) + k3
The Attempt at a Solution
The left side is easy:
L[v’(t)] = sV(s) - v(0)
But I’ve been stumped by the right side. Specifically, I am having trouble finding the L[v(t)^2] term. I’ve tried substituting into the definition of the LT and integrating by parts but not luck so far and can't find an similar example on the web or in a table... Any suggestions?