The flow of linear momentum
([T.sup.33]) is positive in the first region and then jumps up on the first boundary due to the jump of the current j.
The motion is assumed to be one-dimensional, due to the conservation of the linear momentum
[1, 7, 8, 14-17].
Let the entire space be divided into small regions of dimension [delta]x = [delta]y = [delta]z = [delta]l, where [delta]l is sufficiently small that any of the momentum densities, [[??].sub.pi] (x, y, z, t), can be considered constant within each region so that [[??].sub.pi](x, y, z, t) [delta][l.sup.3] is a linear momentum
propagating at c in a definite direction in space.
where [mathematical expression not reproducible] are, respectively, the components of the linear momentum
P in the spaces, [mathematical expression not reproducible] are all real.
Collecting all the results, Eqs (31)-(34), and substituting them into the balance of linear momentum
(29), we arrive at the dispersive wave equation in the form
As a result, the centroidal dynamics can be indirectly stabilized using a simple VRPbased control law to regulate the DCM position where the commanded VRP is mapped to a corresponding linear momentum
rate of change objective using Eq.
By referring to the resolved momentum control, the total momentum, including linear momentum
P and angular momentum L, can be defined as 
[K.sub.l] = linear momentum
resistance coefficient, 1/s
equation in the radial direction for the gaseous phase:
Analysis of reported experimental data  indicates that the forward angular momentum associated with a forward fall is neutralized primarily during the impact phase, whereas the forward and downward linear momentum
associated with a fall was reduced during the postimpact phase.
In this case, as the associated interaction term is negative, the particle phase delivers a linear momentum
to the gas in the axial direction, decreasing the velocity of the particles.
Because the yo-yo is moving in a downward line, it builds up linear momentum
(an object's mass times its velocity); but it also gains angular momentum, or momentum from rotating.