ABSTRACT
This chapter shows that certain second-order equations with constant coefficients, certain Bessel equations, the Legendre equation, and the hypergeometric equation each with homogeneous boundary conditions are Sturm–Liouville systems. Eigen functions of a Sturm–Liouville equation satisfying a specific set of homogeneous boundary conditions are orthogonal. There are physical systems that require more than one dependent quantity to describe them. One such system is a beam described by the Timoshenko theory which requires two coupled quantities, one to describe the transverse motion of the beam, and the other the rotation of the beam’s cross section. In this case, one can still generate orthogonal functions under certain conditions. The chapter discusses what these conditions are.
