TABLE OF CONTENTS Another common approach used in solving differential equations is that of Laplace transforms. We will begin with a short review of Laplace transform techniques and then apply these techniques to the six linearized differential equations of motion for the aircraft. The differential operator, P, discussed in Sec. 7.1.1.1, is analogous to the Laplace variable, s. The insight gained with the roots of transformed differential equations obtained using the differential operator will directly transfer to the roots obtained with the Laplace variable, s.
It is assumed that the reader has gained familiarity with solution of differential equations using Laplace transforms from a previous course. It is the intent of this text to simply review highlights of the Laplace method. Simply stated, the Laplace method transforms a linear differential equation from the time domain (the derivatives are with respect to time) into an algebraic equation in the Laplace domain where the variable s is used. We will denote this Laplace transform operation with the symbol L. The methods of algebra are then used in a straightforward manner to solve for the parameter of interest. The resulting equation is transformed back to the time domain, referred to as an inverse Laplace transform operation and denoted with the symbol L ?1 so that the time response can be obtained. By convention, small letters are used to represent functions of time and upper case letters are used...
