Derivatives for differential equation

[Thoreau]

Hello,

My first post here

I have a numerical problem for Matlab but I get stuck with the basic math...

For a circuit I have three equations:

1.Inductance: L=Lo/(1+I^2)
2.Voltage over the inductance: V=L*dI/dt
3.Current over a condensator: I=-C*dV/dt

From this I should be able to derive the second order differential equation:

4. d2/dt2=2I(dI/dt)^2/(1+I^2)-I(1+I^2)/Lo*C

I know I must find the derivative for V, dV/dt and substitute this into I=-C*dV/dt and this should yield equation 4 but I think my derivatives are all wrong!
Basically I need help to use the chain rule (i guess?) and finding the derivative for V=L*dI/dt

This is what I got: dV/dt=dI/dt*(-Lo*2I)/(1+I^2)^2+L*d2/dt2*??? something is wrong...

Would really appreciate the help!

 

[Deleted member 4993]

Hello,

My first post here

I have a numerical problem for Matlab but I get stuck with the basic math...

For a circuit I have three equations:

1.Inductance: L=Lo/(1+I^2)
2.Voltage over the inductance: V=L*dI/dt
3.Current over a condensator: I=-C*dV/dt

From this I should be able to derive the second order differential equation:

4. d²(?)/dt²=2I(dI/dt)^2/(1+I^2)-I(1+I^2)/Lo*C ......... Your problem statement is incomplete.

I know I must find the derivative for V, dV/dt and substitute this into I=-C*dV/dt and this should yield equation 4 but I think my derivatives are all wrong!
Basically I need help to use the chain rule (i guess?) and finding the derivative for V=L*dI/dt

This is what I got: dV/dt=dI/dt*(-Lo*2I)/(1+I^2)^2+L*d2/dt2*??? something is wrong...

Would really appreciate the help!

.

 

[Thoreau]

This is how the differential equation should look like:


4. d2I/dt2=2I(dI/dt)^2/(1+I^2)-I(1+I^2)/Lo*C

 

[Deleted member 4993]

This is how the differential equation should look like:


4. d2I/dt2=2I(dI/dt)^2/(1+I^2)-I(1+I^2)/Lo*C

So start writing:

I = L * dV/dt

dI/dt = ??

d²I/dt² = ???

 

[Thoreau]

So start writing:

I = L * dV/dt

dI/dt = ??

d²I/dt² = ???

I dont get this, why and how can i write I=L*dV/dt?

What I'm looking for is the derivative (dV/dt) for V=L*dI/dt so i can substitute that into I=-C*dV/dt
and this should yield d²I/dt^{2=2I(dI/dt)^2/(1+I^2)-I(1+I^2)/Lo*C}