Foundations of Space Dynamics. Ashish Tewari
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The last term on the right‐hand side of Eq. (2.19) is the change caused by rotating axes,
Since the velocity of the particle could be varying with time, the acceleration,
(2.20)
with the understanding that the derivatives are taken with respect to a stationary reference frame. If the reference frame in which the position and velocity of the particle are resolved is itself moving such that its origin,
Equation (2.21) is an alternative kinematical description of the particle's motion, and can be regarded as being equivalent to that given by Eq. (2.19), which has been differentiated in time according to the chain rule. Equation (2.21) is useful in finding the acceleration of the particle from the position and velocity measured in a moving reference frame. The first two terms on the right‐hand side of Eq. (2.21) represent the net acceleration due to the origin of the moving frame. The term
The application of Newton's second law to the motion of a particle of a fixed mass,
The linear momentum,
(2.23)
Since the particle's mass is constant, the second law of motion given by Eq. (2.22) can alternatively be expressed as follows:
which gives rise to the principle of linear momentum conservation if no force is applied to the particle.
The angular momentum,
(2.25)
By virtue of Eq. (2.24), it is evident that the angular momentum of the particle about o can vary with time, if and only if a torque, defined by
(2.26)
This results in the principle of angular momentum conservation if no torque acts on the particle about o.
The work done on a particle by a force while moving from point A to point B is defined by the following integral of the scalar product of the force,
(2.27)
The application of Newton's second law for the constant mass particle, Eq. (2.22), results in the following expression for the work done:
(2.28)
where