Any point that is rigidly connected to the body can be used as reference point ( origin of coordinate system " L " ) to describe the linear motion of the body ( the linear position, velocity and acceleration vectors depend on the choice ).
32.
If the direction upward is taken as positive ( the normal cartesian convention ) then " positive " g-force ( an acceleration vector that points upward ) produces a force / weight on any mass, that acts " downward " ( an example is positive-g acceleration of a rocket launch, producing downward weight ).
33.
In the same way that we found the Lema�tre observers, we can boost our static frame in the \ vec { e } _ 3 direction by an undetermined parameter ( depending on the radial coordinate ), compute the acceleration vector, and require that this vanish " in the equatorial plane " \ theta = \ pi / 2.
34.
Where "'F "'is the vector sum of all forces exerted on the vehicle, m is its current mass, and "'a "'is the acceleration vector, the instantaneous rate of change of velocity ( "'v "'), which in turn is the instantaneous rate of change of displacement.
35.
Computing the kinematic decomposition of the timelike congruence defined by the timelike unit vector field \ scriptstyle \ vec { f } _ 0, we find that the expansion and vorticity again vanishes, and in addition the acceleration vector vanishes, \ scriptstyle \ nabla _ { \ vec { f } _ 0 } \ vec { f } _ 0 \; = \; 0.
36.
In the same way, a " negative-g force " is an acceleration vector " downward " ( the negative direction on the y axis ), and this acceleration downward produces a weight-force in a direction " upward " ( thus pulling a pilot upward out of the seat, and forcing blood toward the head of a normally oriented pilot ).
37.
Here \ boldsymbol { U } is the velocity field of the air, \ boldsymbol { \ Omega } is the angular velocity vector of the planet, \ rho is the density of the air, p is the air pressure, \ boldsymbol { F } _ r is the friction, \ boldsymbol { g } is the acceleration vector due to gravity and { D \; \ over Dt } is the material derivative.
