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NOMENCLATURE A z launch azimuth (deg) d T distance of thrust location from vehicle longitudinal axis (m) h Altitude of separation (km) I Inertia tensor (kg-m 2 ) l CG distance of CG from nose tip along longitudinal axis (m) l T distance of thrust location from nose tip along longitudinal axis(m) m M , m S mass of the ongoing and spent bodies (kg) m propellant mass flow rate (kgs -1 ) R E , R P , R S Earth's equatorial radius, polar radius, radius at the surface (km) r, q, p body angular rates yaw, pitch and roll (deg/s) r I position vector in ECI frame (X I , Y I , Z I ) (m) r CG position vector of the body CG offset (m) r s spring location from CG (m) r T distance of thrust location from main body CG (m) t time (s) T thrust (N) v velocity in the body frame (ms -1 ) X, Y, Z body axes yaw, pitch and roll δ spring mounting azimuth angle (deg) ABSTRACTThis paper presents a systematic formulation for the simulation of rigid body dynamics, including the short period dynamics, inherent to stage separation and jettisoning parts of a satellite launcher. This also gives a review of various types of separations involved in a launch vehicle. The problem is sufficiently large and complex; the methodology involves iterations at successively lower levels of abstraction. The best choice to tackle such problems is to use stateof-the-art programming technique known as object oriented programming. The necessary classes have been identified to represent various entities in the launch vehicle separation process (e.g., gravity, aerodynamics, propulsion and separation mechanisms etc.). Simple linkages are modelled with suitable objects. This approach helps the designer to simulate a launch vehicle separation dynamics and also to analyse separation system performance. To examine the influence of the design variables on the separating bodies, statistical analyses have been performed on the upper stage separation process and pull out of ongoing stage nozzle from the spent stage of a multistage rocket carrier using retro rockets.

This paper presents in brief the formulation of the rigid body separation dynamics that are useful for the design and analysis of satellite separation systems using the helical compression spring mechanism. In satellite launch vehicle chronology, safe injection of the satellite into the desirable orbit is an important final task. The body rate of the satellite during separation should be within the satellite control capabilities. The Taguchi method is employed in order to understand the influencing parameters in the separation process. Statistical analysis has been carried out to identify the probability distribution function for reliability and safety assessment of the satellite separation of a launch vehicle. Using the response surface method (RSM), an empirical relation is obtained for the body rate of the satellite in terms of the 28 physical parameters. The RSM results are compared with the Taguchi simulation results. Reliability and safety assessments are made on the satellite separation of a typical launch vehicle.

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