Showing papers on "Multiple-scale analysis published in 1972"
TL;DR: In this paper, a method of multiple scales is developed for the generation of uniformly valid asymptotic solutions of initial value problems for nonlinear wave equations, where the nonlinearities are small and only involve the first derivatives of the dependent variable.
Abstract: A method of multiple scales is developed for the generation of uniformly valid asymptotic solutions of initial value problems for nonlinear wave equations. The method is applicable when the nonlinearities are small and only involve the first derivatives of the dependent variable. The determination of the first approximation is reduced to the solution of a pair of nonlinear, first order, ordinary differential equations. The method is then extended to apply to canonical systems of hyperbolic equations, and to problems in which the nonlinearities also involve the second derivatives of the dependent variable and hence lead to shocks.
72 citations
TL;DR: In this paper, a nonlinear analysis for the motion of a rolling re-entry vehicle for the case of constant roll rate and for variable roll rate, dynamic pressure, and stability derivatives is performed.
Abstract: A nonlinear analysis is performed for the motion of a rolling re-entry vehicle for the case of constant roll rate and for the case of variable roll rate, dynamic pressure, and stability derivatives. Each of the restoring, damping, lag, Magnus, and induced moments is assumed to be a cubic function of the angle-of-attack with variable coefficients. In the constant roll rate case, the derivative expansion version of the method of multiple scales is used to derive equations that characterize the time variation of the amplitudes and phases of the nutation and precession modes. In the variable roll rate case, the generalized version of the method of multiple scales is used to derive equations for the roll rate and the amplitudes and phases of the oscillatory modes of the angle of attack near and away from roll resonance. The roll degree of freedom is coupled with the pitch and yaw degrees of freedom instead of assuming a priori the variation of the roll rate. The analytical solutions are found to be in good agreement with the numerical solutions of the full problem.
22 citations
TL;DR: In this paper, a new set of variables comprising action and angle variables has been introduced for total number-conserving many-boson systems, which are conjugate in the "mean" and provide a rigorous approach to introducing phase variables.
Abstract: Utilizing the facts (i) that the number of particles in the many-boson system is conserved and (ii) that the Hamiltonian is Hermitian, a new set of variables comprising “action” and “angle” variables has been introduced. These variables are conjugate in the “mean” and provide a rigorous approach to introducing phase variables for “total-number-conserving many-boson systems.”
5 citations