and integrating, supposing V the velocity and a the angle of projection, P=√2 2 sec3μdp=2 √√1+p3dp =p√1+p2+ log (p+ √1+p3). The equations of motion are, resolving horizontally and vertically, If S, s denote the arcs of the trajectory in a non-resisting and a resisting medium, measured from the point of projection to any two points at which the tangents are parallel; then, since in the non-resisting medium a∞, = therefore 217. For a flat trajectory, p being always small, we may ds put = 1, and then equation (5) may be written dx or Integrating, 2 V2 cos2a 2 V3 cos2a; α 2 g tan a. V2 cos2 a α Multiplying by e and integrating, 2008a+ (2008a+ tan a)e, -2x ga V2 cos2 ga cos2 dx of which the first two terms will represent the trajectory in a non-resisting medium. R 218. A particle moves in a resisting medium under a central attraction; to determine the orbit. Let P be the acceleration due to the central attraction, R the retardation due to the resistance of the medium; then resolving along and perpendicular to the radius vector, an equation of the same form as that for the motion in a non-resisting medium, h however being now variable. 219. If in addition to the central attraction, there is R a transversal force producing acceleration T, we shall obtain the equation analogous to (5) most simply by resolving in the normal, and then an equation of the same form as that obtained in § 136. S |
