Rectilinear and Rotational Motion

[phiska]

Landing Gear of an aircraft can be modeled as a wheel with damper and spring attached horizontally.

I have to show that the equation of motion is given by
(I+mr^2)a + cr^2v + kr^2x = 0

where a= acceleration, v= velocity, x= displacement and spring stiffness = k and damping coefficient = c.

I realize i have use resultant forces = ma, and then substitute for friction into the sum of moments about the centre= 0.5(mr^2).

However, when i do this, i get an extra mr^3xtheta(double dot).

Am i missing the point with respect to intial conditions or is my maths just all over the place?

Help!

Cheers

 

[Andrew Mason]

Landing Gear of an aircraft can be modeled as a wheel with damper and spring attached horizontally.

I have to show that the equation of motion is given by
(I+mr^2)a + cr^2v + kr^2x = 0

where a= acceleration, v= velocity, x= displacement and spring stiffness = k and damping coefficient = c.

It looks to me like you are trying to describe the equation of motion of the centre of mass of the wheel. Is r the radius of the wheel? What is the mass, m? It looks like the mass of the wheel only. What about the mass of the rest of the gear (eg. spring)?

AM

 

[phiska]

mass of wheel, m, radius of wheel, r, mass of spring and damper not considered and no mass of rest of landing gear.

Also, wheel should roll without slipping.