Choice of Nomenclature

The choice of which symbol represents which variable is often difficult. The English alphabet having but 26 letters can be augmented by the Greek one. See Table 9.2. The Greek upper case letters are usually restricted to describe functions. There are many upper case Greek letters that are the same as the Latin ones (alpha, beta, epsilon, etc.). The commonly used mathematical functions or operators are also given.

The International Organization for Standardization, ISO, has published many standards giving the nomenclature to be used in certain fields of study. It also has defined what SI should be. All of these standards are available in Quantities and Units [2].

Table 9.2: The Letters of the Greek Alphabet Used in the Typesetting of Equations

Name	Lower case	Upper case	Function or Operator
Alpha	$\alpha$	A
Beta	$\beta$	B	Beta function
Gamma	$\gamma$	$\Gamma$	Gamma function
Delta	$\delta$	$\Delta$	Increment
Epsilon	$\epsilon$ , $\varepsilon$	E
Zeta	$\zeta$	Z
Eta	$\eta$	H
Theta	$\theta$ , $\vartheta$	$\Theta$
Iota	$\iota$	I
Kappa	$\kappa$	K
Lambda	$\lambda$	$\Lambda$
Mu	$\mu$	M
Nu	$\nu$	N	Newman
Xi	$\xi$	$\Xi$
Omicron	o	O
Pi	$\pi$ , $\varpi$	$\Pi$	Multiplication
Rho	$\rho$ , $\varrho$	P	Legendre polynomials
Sigma	$\sigma$ , $\varsigma$	$\Sigma$	Summation
Tau	$\tau$	T
Upsilon	$\upsilon$	$\Upsilon$
Phi	$\phi$ , $\varphi$	$\Phi$
Chi	$\chi$	X
Psi	$\psi$	$\Psi$
Omega	$\omega$	$\Omega$

A part from those given in Table 9.2, many operators have been attached to certain symbols. Those common in mechanical engineering are given in Table 9.3. Also included in that table are the preferred ways of writing certain functions. The variable $x$ is used to clarify the notation.

Table 9.3: Common engineering operators or functions

Operator/Function	Symbol	Notes
prime	$x'$	first derivative with respect to a length
double prime	$x''$	second derivative with respect to a length
dot	$\dot{x}$	first derivative with respect to time
double dot	$\ddot{x}$	second derivative with respect to time
10 base logarithm	$\lg x$	$\log_{10} x$ is sometimes used
natural logarithm	$\ln x$
inverse trigonometric	$\arctan\left(x\right)$	Do not use $\tan^{-1}$ because of confusion
		with the reciprocal $\frac{1}{\tan\left(x\right)}$