I normalized vd and il to put in a state plane diagram. I have an id/Ibase term in my dm/d_theta equation. What do I do with this? I can't make j = (il-id)/Ibase because that would affect my dj/d_theta equation.
On slide 15 of lecture 16, how did Prof. Maksimovic derive m(theta)=1+A*cos(theta + theta_0) and j(theta)=J-A*sin(theta+theta_0)?
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On slide 15 he solved the geometry of the circle - the initial condition 'theta_not' being the datum. Note that theta_not may not align with either the x or y axis. Theta is measured from theta_not in the direction shown. Therefore the initial condition is in the fourth quadrant of the circular trajectory, i.e. below J and above m=1. Hope this helps.
...actually Lec 17 page 6 hand written note has this derivation
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