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Numerical Evaluation of Integrals
Differential Equations of the First Order
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according to Eq aileron airplane amplitude angle angular velocity applied approximation arbitrary constant axes axial axis beam Bessel functions boundary conditions buckling calculate called center of gravity Chapter characteristic equation coefficients column complex components consider const corresponding cosh damping deflection degrees of freedom denote determined difference disks displacement elastic electromotive force elliptic integral equations of motion equilibrium position example expression external forces finite fixed Fourier series given gyroscope harmonic Hence homogeneous equation horizontal impedance inertia infinite number integral curves kinetic energy Lagrange's equations length Let us assume load mass point method mode of oscillation momentum normal modes obtain parameter particular solution pendulum plane potential energy principal oscillations problem represents roots rotation satisfy seen shaft sin2 sinh solution of Eq spring constant Substituting tion trigonometric trigonometric functions values variable vector vertical vibration voltage write