Recent content by ceomtcl

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    Gravitation (Preliminary Reference Earth Model)

    Thanks Redbelly98! I did this problem. However I am having another problem in an associated problem with this question. I am working it out, however if I get stuck then i would ask you to help me. Thanks once again!
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    Gravitation (Preliminary Reference Earth Model)

    Homework Statement Assuming that we know the density of Earth as a function of radius, we have to derive the equation for gravity as the function of radius. Homework Equations The Attempt at a Solution lets us choose density as \rho(r). I know that within a hollow sphere there is no gravity...
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    Stability Classification: How to Determine if a System is Asymptotically Stable?

    Moreover, will a "center" be referred to as a stable or unstable equilibrium?
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    Stability Classification: How to Determine if a System is Asymptotically Stable?

    This can be evaluated by considering real part of eigenvalues < 0. But can you let me visualize it conceptually?
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    Stability Classification: How to Determine if a System is Asymptotically Stable?

    Homework Statement How can i classify (1) stable node (2) saddle and (3) center as either (a) stable or asymptotically stable? Homework Equations <None> The Attempt at a Solution All three are stable. Stable node seems to be asymptotically stable. But I am not...
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    When is an Equilibrium Point Isolated in a Simple Linear Time Invariant System?

    ok, i think i understood it, Thanks a lot for the help!
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    When is an Equilibrium Point Isolated in a Simple Linear Time Invariant System?

    Does it mean that the Equilibrium point is isolated when it is stable?
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    When is an Equilibrium Point Isolated in a Simple Linear Time Invariant System?

    I know that the linear system can have only one isolated equilibrium point, thus it can have only one steady state operating point that attracts the state of the system irrespective of the initial state. However a non linear system can have more than one isolated equilibrium point.
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    When is an Equilibrium Point Isolated in a Simple Linear Time Invariant System?

    Can you please redefine it for me? may be i am missing something important?
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    When is an Equilibrium Point Isolated in a Simple Linear Time Invariant System?

    Homework Statement Given a simplest linear time invariant system (x dot = Ax), with an Equilibrium Point at the origin; when is the Equilibrium Point isolated? Homework Equations None The Attempt at a Solution Conceptual Question
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    Lyapunov Theory: Find Unique Equil Pt.

    So, the blank should be "only". Just wanted to confirm if it is what you want to say.
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    Lyapunov Theory: Find Unique Equil Pt.

    1. I believe that if the point x=0 is a "globally asymptotically stable equilibrium point" then if we approach x=0 from any direction then it will converge to equilibrium point. Am I right? 2. According to me, there is no other equilibrium point. Please let me know if i am right?
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    Lyapunov Theory: Find Unique Equil Pt.

    I have around 50 such objective questions for the assignments. I am done with 40 plus, but a few of these are haunting ms and i am not sure about them! Any help is highly appreciated!
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    Lyapunov Theory: Find Unique Equil Pt.

    Lyapunov Theory: Please Help! Homework Statement If the origin x=0 is globally asymptotically stable equilibrium point of the system then it must be the _________ equilibrium point of the system. Homework Equations None The Attempt at a Solution This is an objective/one word answer.
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