TireBalance - % File: TireBalance.al % Autolev program to...

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Sheet1 Page 1 % File: TireBalance.al % Autolev program to interpret inertia matrices using % balancing of a car tire as an example. % Calculate the inertia dyadic for a wheel B modeled as % a thin cylinder. % Then add a particle P1 to the wheel at some location to alter % the inertia dyadic. % Finally add another particle P2 at the correct location % to cause the off-diagonal terms on the inertia dyadic to % disappear. % For each of these three configurations, also derive the % dynamics equations for the wheel connected to ground by % a ball-and-socket joint, and calculate the generalized % accelerations for a constant torque input about the % wheel axis. Demonstrate that % 1) For the original wheel, torque about the wheel axis % produces generalized accelerations only about that axis, % 2) For the wheel plus particle P1, torque about the wheel % axis produces generalized accelerations about ALL axes, % and % 3) For the wheel plus particles P1 and P2, torque about the % wheel axis again produces generalized accelerations only % about that axis, %-------------------------------------------------------------------- % Set up problem AutoOverwrite On NewtonianFrame N % Nx> to the right, Ny> up, and Nz> = Nx> x Ny> RigidBody B RigidFrame C,D Particle P1,P2 Point O Constant mB,r,h Constant mP1,x1,y1,z1 Constant mP2,x2,y2,z2 Variable q1'',q2'',q3'' Constant Tz %-------------------------------------------------------------------- % Inertia derivations % Inertia dyadic for body B relative to Bcm Ixx = (1/12)*mB*(3*r^2+h^2) Iyy = (1/12)*mB*(3*r^2+h^2) Izz = (1/2)*mB*r^2 I_B_Bcm>> = Ixx*Bx>*Bx> + Iyy*By>*By> + Izz*Bz>*Bz> Explicit(I_B_Bcm>>) I_B_Bcm_Mat = Represent(I_B_Bcm>>,B) % Inertia dyadic for a particle of mass B situated at Bcm relative to O p_O_Bcm> = -0.5*h*Bz> I_Bcm_O>>=mB*(1>>*dot(p_O_Bcm>,p_O_Bcm>)-p_O_Bcm>*p_O_Bcm>)
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This note was uploaded on 06/13/2011 for the course EGM 3400 taught by Professor Matthews during the Spring '08 term at University of Florida.

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TireBalance - % File: TireBalance.al % Autolev program to...

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