| || Application of Discrete Maximum Principle to Optimization Problem of Multiple Stage Rockets
Author : Tawakley, V.B.;Jain, S.C.
Source : Defence Science Journal ; Vol:18(3) ; 1968 ; pp 161-172
Subject : 629.76 Rockets and Missiles
Keywords : Gravity;Optimization
Abstract : The Discrete Maximum Principle has been applied to solve a few optimization problems of multiple staged rockets by including the gravity into the performance equations. The problem of finding the minimum mass in order to obtain a specified velocity at the end of powered phase has been solved under various assumptions about the structure factors both when the stages are arranged in series as well as in parallel. The problem when the objective function to be minimised is the cost per pound of the payload has also been investigated.
| || Stability of Rocket Flight during Burning
Author : Srivastava, T.N.;Singh, Manak
Source : Defence Science Journal ; Vol:17(4) ; 1967 ; pp 215-222
Subject : 629.76 Rockets and Missiles ;629.762 Missiles
Keywords : Gravity;Aerodynamic Forces;Torques
Abstract : Stability of the rocket motion during burning is discussed taking into consideration gravity, aerodynamic forces and torques. Conditions for stabilizing the rocket motion are investigated. Analysis for initial and final phases of burning is given separately. Stability regions of the projected motions on two dimensional co-ordinate planes are obtained and thereby stability region of the actual motion is derived. Stability diagrams illustrate statically and dynamically stable and unstable regions.
| || Gravitational Effect of the Shape of a Bubble Formed by an Under Water Explosion
Author : Bhatia, P.C. ;Bahl, S.K.
Source : Defence Science Journal ; Vol:19(2) ; 1969 ; pp 121-128
Subject : 623 Military Science and Engineering
Keywords : Gravity ;Gas bubble
Abstract : The shape of a gas bubble initially formed by an explosion or by some other means in a liquid just before it starts to move upwards has been determinded by considering surface tension and the pressure on the interface. The external pressure is taken to be non-uniform due to the presence of gravity and the internal pressure is assumed to be constant. Two cases have been considered. In the first case of a two-dimensional bubble an exact solution has been obtained whereas in the case of a three-dimensional bubble only an approximate solution could be found.