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q, the dynamic pressure, is equal to 1/2 ρv 2, where ρ is atmospheric density, modeled for Earth as a function of altitude in the International Standard Atmosphere (using an assumed temperature distribution, hydrostatic pressure variation, and the ideal gas law); and
Law 1. A body continues in its state of rest, or in uniform motion in a straight line, unless acted upon by a force. Law 2. A body acted upon by a force moves in such a manner that the time rate of change of momentum equals the force. Law 3. If two bodies exert forces on each other, these forces are equal in magnitude and opposite in direction.
2.1.3 Angle of elevation. 2.2 ... it may be necessary to account for nonuniform gravitational forces and ... giving the maximum range can be found by ...
Flight path angle γ: is the angle between horizontal and the velocity vector, which describes whether the aircraft is climbing or descending. Bank angle μ: represents a rotation of the lift force around the velocity vector, which may indicate whether the airplane is turning .
The left hand side of the equation—which includes the sum of external forces, and the sum of external moments about P—describes a spatial wrench, see screw theory. The inertial terms are contained in the spatial inertia matrix
Stability derivatives, and also control derivatives, are measures of how particular forces and moments on an aircraft change as other parameters related to stability change (parameters such as airspeed, altitude, angle of attack, etc.). For a defined "trim" flight condition, changes and oscillations occur in these parameters.
The angles UCP and VCQ both equal θ 1, whereas the black arc represents the angle UCQ, which equals θ 2 = k θ 1. The solid ellipse has rotated relative to the dashed ellipse by the angle UCV, which equals (k−1) θ 1. All three planets (red, blue and green) are at the same distance r from the center of force C.
We can see that the range will be maximum when the value of is the highest (i.e. when it is equal to 1). Clearly, 2 θ {\displaystyle 2\theta } has to be 90 degrees. That is to say, θ {\displaystyle \theta } is 45 degrees.