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Investigating how a car bounces with the framework of an idealized model. Let the chassis be a rigid, square plate, of side a and mass M, whose corners are supported by massless springs, with spring constants K,K,K and k < K (the faulty one). The springs are confined so they stretch and compress vertically, with unperturbed length L. The density of the plate is uniform.

(a) explain why the system has 3 generalized co-ordinates to be described completely.

1 translational ( up and down ) and 2 rotational.

(b) show your coordinates.

http://img11.imageshack.us/img11/1859/coordsd.jpg [Broken]

(c) Derive the Lagrangian for the system assuming that all motions are small and the four springs are identical.

This is where I'm stuck.....

L = KE + PE

KE = .5mv^2 + .5I(phi dot)^2 + .5I(theta dot)^2

where v = velocity of the centre of mass.

phi dot is the derivative of phi (does this give you the angular velocity?)

theta dot is the derivative of theta

I is the moment of inertia of a square plate (Ma^2)/12

PE = 4.(.5kz^2) = 2kz^2

Is this even remotely correct? Any help as always is greatly appreciated.

(a) explain why the system has 3 generalized co-ordinates to be described completely.

1 translational ( up and down ) and 2 rotational.

(b) show your coordinates.

http://img11.imageshack.us/img11/1859/coordsd.jpg [Broken]

(c) Derive the Lagrangian for the system assuming that all motions are small and the four springs are identical.

This is where I'm stuck.....

L = KE + PE

KE = .5mv^2 + .5I(phi dot)^2 + .5I(theta dot)^2

where v = velocity of the centre of mass.

phi dot is the derivative of phi (does this give you the angular velocity?)

theta dot is the derivative of theta

I is the moment of inertia of a square plate (Ma^2)/12

PE = 4.(.5kz^2) = 2kz^2

Is this even remotely correct? Any help as always is greatly appreciated.

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