00:01
As per the question we are given with the equations for orbit plane motion, orbit plane motions of a satellite in orbit.
00:10
These equations are that r double dot minus theta square r is equals to minus mu divided by r square plus u1.
00:24
R for theta double dot plus 2r theta theta is equal to u2.
00:31
Now these u1 and u2 are the control inputs for the satellite.
00:41
For the part 1, we are asked to obtain a state space model of a non -linear system dynamics where state vectors are defined as, it is given to us as x is equals to x1, x1 then x2 then x3 then x4 all raised to the power r which is equals to r theta r dot theta dot raised to the power t.
01:11
This is given to us.
01:14
Now according to this, as were the given questions or equations, r double dot is equal to theta square r minus neo r square plus u1.
01:27
This is now your equation 1.
01:29
We have turned equation 1 by transferring theta to right hand side.
01:34
Second equation becomes that theta double dot will be equal to u2 divided by r minus 2r theta divided by r.
01:48
This will be the second equation that has been now changed.
01:51
Now these two equations, according to these two equations, we have already given that as per part x1, x2, x3 and x4.
02:01
These are according to the question equal to r then theta then r dot and theta dot.
02:10
This is given to us.
02:12
Now because according to this, first of all consider this equation 1 and 2.
02:19
According to these given values, x1 dot will be equal to x3, right? similarly, x2 dot will be equal to x4.
02:30
Therefore, we can say that x3...