Equations of rotational motion:

Differential equations can be derived for studying the effects of either nonconservative or conservative torques on the attitude motion of a tumbling triaxial rigid satellite. These equations, which are analogous to the Lagrange planetary equations for the osculating elements, are then used to study the attitude motions of a swiftly spinning, rigid satellite about its center of mass, which, in turn, is constrained to move in the elliptical orbit about an attracting point mass. Similar to the 4 basic equations which describe the motion of a body moving with the constant acceleration the rotational forms are as follows:

ω = ω₀ + αt

ω² = ω²₀+ 2αθ

θ = ω₀t + 1/2 αt²

 Here

ω₀ = angular velocity at the time t=0s [rads^-1]

ω = angular velocity at the time t [rads^-1]

α = constant angular acceleration [rads^-2]

θ = angle turned through in the time t [rad]

             t = time [s]

The body is considered between 2 instants in time: one initial point and one current point. If a is constant, a differential, a dt, can be integrated over the interval from 0 to Δt (Δt = t - t_i), to obtain a linear relationship for velocity. Integration of the velocity yields a quadratic relationship for position at the end of interval.

v = v_i + αΔt