The Mechanical Principles of the Aeroplane

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There are six unknown quantities, which are to be determined by these equations and which define the motion of the parachute. These are w 19 u 2, M 3, 0, <, ^. Now w 2 only occurs in the second equation, and this equation only involves M 2, since b y is a constant which is presumably known. Also -^ only occurs in the fifth equation, and this equation only involves ^, since e^ is a known constant. Thus the second equation determines u 2 completely, and the fifth equation determines -^ completely....
OF THE AEROPLANE 119 Further, u and only occur in the first and sixth equations, and these equations only involve w x and 0. Hence u^ and 6 are completely determined by these two equations. Finally, u s and are completely determined by the second and fourth equations.
The disturbed motion is thus given by 2 = w 20 e *, -^. = o> 2 = o> 20 e ; (140) (141) ( Ar t )M 3 + (Z) 2 + fc^D ) =0 J ' ^ 142) wher'e // 20 is the value of u 2 at t = 0, to, the value of o> 2 or d^rldt at = 0, andZ> = We may assume a priori that b y and 2 are both positive, so that an increased downward velocity gives an increased upward air pressure, and a rotation about a vertical axis is opposed by a sort of frictional resistance.


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