Rectilinear and Rotational Motion

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SUMMARY

The discussion centers on modeling the landing gear of an aircraft as a wheel with an attached damper and spring. The equation of motion is established as (I + mr²)a + cr²v + kr²x = 0, where 'a' represents acceleration, 'v' is velocity, 'x' denotes displacement, 'k' is spring stiffness, and 'c' is the damping coefficient. Participants clarify that the mass 'm' refers solely to the wheel, and the radius 'r' is the wheel's radius. Additionally, it is emphasized that the wheel must roll without slipping for accurate modeling.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with rotational dynamics and moment of inertia
  • Knowledge of spring-damper systems in mechanical engineering
  • Basic calculus for analyzing motion equations
NEXT STEPS
  • Study the derivation of equations of motion for rotational systems
  • Explore the principles of rolling motion and friction in mechanics
  • Learn about the dynamics of spring-damper systems in mechanical applications
  • Investigate the effects of initial conditions on dynamic systems
USEFUL FOR

Mechanical engineers, aerospace engineers, and students studying dynamics and mechanical systems will benefit from this discussion, particularly those focused on modeling and analyzing the motion of landing gear systems.

phiska
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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
 
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phiska said:
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
 
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.
 

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