- #1

- 6

- 0

- Thread starter Rohin.T.Narayan
- Start date

- #1

- 6

- 0

- #2

- 9,908

- 1,089

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

Science Advisor

- 1,075

- 1

Regards,

Reilly Atkinson

- #4

Pengwuino

Gold Member

- 4,989

- 16

Would this be an application in Differential Geometry?

- Last Post

- Replies
- 1

- Views
- 2K

- Replies
- 15

- Views
- 13K

- Last Post

- Replies
- 6

- Views
- 3K

- Last Post

- Replies
- 1

- Views
- 3K

- Last Post

- Replies
- 1

- Views
- 2K

- Last Post

- Replies
- 2

- Views
- 2K

- Last Post

- Replies
- 2

- Views
- 1K

- Replies
- 2

- Views
- 552

- Last Post

- Replies
- 4

- Views
- 3K

- Last Post

- Replies
- 3

- Views
- 3K