Theory of Stability of Motion |
Contents
Introduction | v |
Criterion of stability as a first approximation | 47 |
Par 21 | 57 |
17 other sections not shown
Other editions - View all
Common terms and phrases
A₁ analytical functions approximation arbitrarily small arbitrary constant asymptotically stable become zero begin with terms characteristic equation characteristic numbers consequently defined definite with respect derivative determined different from zero differential equations dx dt equa equal to zero equations of disturbed finite following inequality initial conditions integral curves Let us assume Let us consider Let us suppose linear equations Lyapunoff's functions m-th order m₁ magnitude method motion is unstable negative real negative-definite obviously origin of coordinates periodic coefficients periodic functions periodic solution polynomials positive number positive-definite positive-definite function preceding paragraph problem of stability pure imaginary roots quadratic form quantity region of stability resolutions respect to sign right-hand sides root equal roots of equation satisfy the inequalities second order solutions of equations stabilized motions substitution sufficiently small system of equations system of linear theorem tions transformation turbed undisturbed motion v₁ x₁ y₁