Abstract
Equations of motion of an elastic rocket are given using an extension of Kane’s method with an efficient choice of generalized speeds. The modal integrals are updated for the time-time-varying mass of the rocket by Hermite interpolation. The formulation includes geometric softening due to thrust and is suitable for nonlinear control design of a flexible booster vehicle.
Highlights
Equations of motion of an elastic rocket are given using an extension of Kane’s method with an efficient choice of generalized speeds
Renders Equation (4) free of the vibration mode coordinates, qj, Equation (10) is expressed in terms of eight modal integrals leading to the simplification: matrices, the elements of which are of the following form, that can be n
We have extended Kane’s equations for variable mass to flexible bodies, to simulate the dynamics of a flexible rocket
Summary
Equations of motion of an elastic rocket are given using an extension of Kane’s method with an efficient choice of generalized speeds. Basic dynamics of rockets has been well understood for a long time [1]. In this short Note we focus on the effects of flexibility of long slender rockets, and in particular on possibilities of buckling due to thrust on an elastic booster vehicle with rapid mass loss. Use of assumed vibration modes of the body, defined in frame B, yields for the position and velocity of a particle P of the body, Kane’s equations for variable mass, can be formed by extending those for the particle model of [5] to flexible bodies, and are written for the 6+n generalized speeds as follows: n. Introducing efficient generalized speeds [4], for elastic deformation, σ j associated with the j-th mode of vibration, n n n
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
