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Rohin.T.Narayan

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- Thread starter Rohin.T.Narayan
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Rohin.T.Narayan

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For this simple problem, the Lagrangian L of the missile will be the kinetic energy T in an earth-centered inertial frame minus the potential enregy V in an ECI frame.

Then you use Lagrange's equations to get the equations of motion for the missile.

There's an overview at the Wikipedia

http://en.wikipedia.org/wiki/Lagrangian_mechanics

it may not be clear enough if you are not familiar with the subject. You may have to consult a textbook if you want a really detailed explanation. The quick overview is that you have a function L, called the Lagrangian which is written in the form

L(x, x', t), where x is is a coordinate, x' is it's time derivative, and t is time.

Then Lagrange's equations give you the equations of motion directly from the Lagrangian

[tex]

\frac{d}{dt}\left(\frac{\partial L}{\partial x'}\right) =\frac{\partial L}{\partial x}

[/tex]

A simple example - in cartesian coordinates in a potential V with only one coordinate x

L(x,x') = .5*m*x'^2 - V(x)

(note that this is kinetic energy minus potential energy).

Then

d/dt(m*x') = -[itex]\partial V/\partial x[/itex]

For systems with more than one coordinate, there is one Lagrange's equation for each independent coordiante (variable).

- #3

reilly

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Regards,

Reilly Atkinson

- #4

Pengwuino

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Would this be an application in Differential Geometry?

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