[J.sub.wi] - Mass moment of inertia
of the front and rear tyres.
For a flat plate of thickness h in 2D motion, [mathematical expression not reproducible], and the mass moment of inertia
[J.sub.mot] - motor mass moment of inertia
The InertiaFromUpstream signal is the reduced mass moment of inertia
of all the upstream components.
And the frequency also increases with the increment of the rotary mass moment of inertia
for the additional mass compared to the beam, which is defined as the parameter [[alpha].sub.j].
The terms involving the polar mass moment of inertia
([I.sub.p]) are known as gyroscopic moments.
in which W is the tool weight, r is the distance between COG and the suspension, [phi] is the angular displacement, [phi] is the angular acceleration, and I is the mass moment of inertia
. For small oscillations, sin[phi] can be approximated as [phi].
where [J.sub.[summation]]--summary reduced mass moment of inertia
, kg x [m.sup.2], [R.sub.a]--armature's winding's resistance, Ohm, [k.sub.m]--torque factor of the DC motor, N x m/A, [k.sub.e]--coefficient of EMF of the DC motor, V x s/rad.
The flexible arm, with length l, mass per unit length [rho] , mass moment of inertia
[I.sub.[rho]], cross sectional area A, area moment of inertia I, Young's modulus E, shear modulus G, and shear coefficient [kappa], satisfies the Timoshenko beam hypothesis.
in which [I.sub.b], [G.sub.b] [J.sub.b] [C.sub.bt], and [gamma](x, t) represent the mass moment of inertia
per unit length, torsional rigidity, distributed viscous damping to rotational motion, and torsional function of bridge, respectively.