1. Consider the 2nd order autonomous system Y (1) dr dt dy dt av ?? ?? (2) where the potential V is given by V(2) = 12 2 23 + (3) 3 and C is some constant that will given later. (a) (5 points) Find all equilibrium points of the system of differential equations and classify them as either Lyapunov stable (LS), Asymptotically Stable (AS), or Unst

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1. Consider the 2nd order autonomous system
Y
(1)
dr
dt
dy
dt
av
??
??
(2)
where the potential V is given by
V(2) =
12
2
23
+

(b) (5 points) For C = 0, solve
I
.22
dy
dr
(4)
Y
and write down the equation of the curve (2, y(2)) passing through the poin

(c) (5 points) When does the curve cross (1, y(x) = 0) other than at (x, y) = (0,0)?
(
x(y

1. Consider the 2nd order autonomous system Y (1) dr dt dy dt av ?? ?? (2) where the potential V is given by V(2) = 12 2 23 + (3) 3 and C is some constant that will given later. (a) (5 points) Find all equilibrium points of the system of differential equations and classify them as either Lyapunov stable (LS), Asymptotically Stable (AS), or Unstable (U). Equilibrium Point C = 0; LS, AS, U? C=0.2; LS, AS, U? (b) (5 points) For C = 0, solve I .22 dy dr (4) Y and write down the equation of the curve (2, y(2)) passing through the point (0,0). (c) (5 points) When does the curve cross (1, y(x) = 0) other than at (x, y) = (0,0)? ( x(y

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(Solved): 1. Consider the 2nd order autonomous system Y (1) dr dt dy dt av (2) where the potenti ...

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