38 lines
1.8 KiB
TeX
38 lines
1.8 KiB
TeX
\section{Notation Glossary}
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\label{app:notation}
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This appendix provides a glossary of notation used throughout the handbook.
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\nomenclature{$y$}{Dependent variable; unknown function}
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\nomenclature{$y(t)$}{Dependent variable as a function of time $t$}
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\nomenclature{$y(x)$}{Dependent variable as a function of spatial variable $x$}
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\nomenclature{$x$}{Independent variable (spatial)}
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\nomenclature{$t$}{Independent variable (time)}
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\nomenclature{$\lambda$}{Eigenvalue; parameter in characteristic equation}
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\nomenclature{$\omega$}{Angular frequency}
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\nomenclature{$\omega_0$}{Natural angular frequency}
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\nomenclature{$\alpha, \beta, \gamma$}{General constants; damping ratio}
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\nomenclature{$\delta$}{Dirac delta function}
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\nomenclature{$\mu$}{Separation constant; parameter}
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\nomenclature{$\theta$}{Angle; phase shift}
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\nomenclature{$\phi$}{Eigenfunction; angle}
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\nomenclature{$A, B, C$}{General constants of integration}
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\nomenclature{$a, b, c$}{Coefficients in differential equations}
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\nomenclature{$n, m, k$}{Integer indices}
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\nomenclature{$f(t)$}{Input/forcing function}
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\nomenclature{$F(s)$}{Laplace transform of $f(t)$}
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\nomenclature{$\mathcal{L}$}{Laplace transform operator}
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\nomenclature{$\mathcal{L}^{-1}$}{Inverse Laplace transform}
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\nomenclature{$\mathcal{F}$}{Fourier transform operator}
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\nomenclature{$u(t)$}{Unit step (Heaviside) function}
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\nomenclature{$y_h$}{Homogeneous solution}
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\nomenclature{$y_p$}{Particular solution}
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\nomenclature{$W(y_1, y_2)$}{Wronskian of $y_1$ and $y_2$}
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\nomenclature{$\mathbf{A}$}{Coefficient matrix in systems}
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\nomenclature{$\mathbf{x}(t)$}{State vector}
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\nomenclature{$I_n$}{Identity matrix of size $n$}
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\nomenclature{$e^{\mathbf{A}t}$}{Matrix exponential}
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\nomenclature{$\mathbf{u}, \mathbf{v}$}{Vectors in phase plane}
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\nomenclature{$u(t-a)$}{Shifted unit step function}
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\nomenclature{$*$}{Convolution operator}
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