An Analysis of a Compound Pendulum Rocket Suspension

Citation

Norris, James Caspar (1951) An Analysis of a Compound Pendulum Rocket Suspension. Engineer's thesis, California Institute of Technology. doi:10.7907/YDS1-JW02. https://resolver.caltech.edu/CaltechETD:etd-03162009-142423

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. This is an investigation of the equations of motion and physical parameters involved in stabilizing the initial flight of a vertically launched rocket by means of a booster rocket pin-connected below the main rocket. The system is designed to stabilize the flight in its early stage before the aerodynamic control surfaces become effective. Stability of the system is dependent on the pendulum action of the booster rocket. The equations of motion were derived from Lagrange's generalized momentum equation. The differential equations thus obtained were not solved but were tested for stability by means of Routh's stability criteria. The ratio of the mass of the main rocket, M[subscript 1], to the mass of the booster rocket, M[subscript 2], was investigated for the two values [...] = 1.5 and [...] = 7.75. The system involving a mass ratio [...] = 7.75 was found to be unstable under all conditions. However, the system involving a mass ratio [...] 1.5 was determined to be stable in the range 1.62 < β < 4.54 x 10[superscript 10], where β is defined as the ratio of the distance [...] from the center of gravity of the booster M[subscript 2] to the pin connecting the strut to the main rocket M[subscript 1], divided by the radius of gyration, k[subscript 2], of the booster M[subscript 2]. In this range, for any given value of, β, stability was uniquely determined by one value of the ratio α = [...], where [...], is the length of the strut from the main rocket M[subscript 1] to the booster rocket M[subscript 2]. Thus, for a given booster, stability is primarily a function of the ratio [...], and for any given [...], is uniquely determined. Although the system was found to be theoretically stable for the mass ratio [...] = 1.5 , the ratio [...] turned out to be of such great magnitude as to make the system entirely impractical for this particular mass ratio.

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