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nagle_differential_equations_ISM_Part5

nagle_differential_equations_ISM_Part5 - (c Show that for...

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(c) Show that, for the asymptotically stable configuration in (b), the second system in (a) becomes a harmonic oscillator problem, and find the frequency of oscillation in terms of I x , I y , I z , and ω 0 . Phobos maintains I y > I x > I z in its orientation with respect to Mars, and has angular frequency of orbit ω 0 = 0 . 82 rad/hr. If ( I x - I z ) /I y = 0 . 23, show that the period of the libration for Phobos (the period with which the side of Phobos facing Mars shakes back and forth) is about 9 hours. 15

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CHAPTER 1: Introduction EXERCISES 1.1: Background 2. This equation is an ODE because it contains no partial derivatives. Since the highest order derivative is d 2 y/dx 2 , the equation is a second order equation. This same term also shows us that the independent variable is x and the dependent variable is y . This equation is linear. 4. This equation is a PDE of the second order because it contains second partial derivatives. x and y are independent variables, and u is the dependent variable. 6. This equation is an ODE of the first order with the independent variable t and the dependent variable x . It is nonlinear.
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