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The Equations and Their Properties
Solutions to Periodic Differential Equations
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amplitude analysis applications approximate basis solutions Bessel function capacitance capacitor Chap characteristic exponent components considered corresponding cut-off frequency derivative described dielectric discrete transition matrix dynamic eigenvalues electric field electron energy exponential expression Floquet Floquet theory Fourier series given harmonics Hill determinant Hill equation IEEE Trans input instability integral interval Ion Phys linear lossless magnitude Math Mathieu equation Mathieu functions McLachlan Meissner equation modulation monopole mass spectrometer natural frequency negative parametric behaviour particular periodic coefficient periodic differential equations periodic function periodically time-varying systems phase potential pump frequency quadrupole mass filter quadrupole mass spectrometer rectangular waveform regions result sawtooth second order systems Sect short time stability shown in Fig shows sinusoid stability boundaries stability diagram step heights structure techniques term time-varying systems trajectory transform trapezoidal waveform type solutions values variable variation varying vector wave propagation waveform waveform coefficient waveguide whereas whilst Wronskian matrix zero