Contents 1 Introduction 1 1.1 Jet Transport Technique 1 1.2 Organization of the Book 5 References 7 2 The Implementation of Jet Transport Software 11 2.1 Polynomial Storage 11 2.2 Polynomial Algebra 14 2.2.1 Basic Polynomial Operations 15 2.2.2 Differential Polynomial Algebra 20 2.2.3 Polynomial Approximation to Univariate Functions 21 2.2.4 Polynomial Approximation to a Multi-variable Function 26 2.2.5 Numerical Simulations 27 2.3 Flow Propagation 29 2.3.1 Parameterization Method 31 2.3.2 Runge-Kutta Methods 33 2.3.3 Semi-analytical Polynomial Propagation 35 2.3.4 Polynomial Evaluation 36 2.3.5 Numerical Simulations 38 References 43 3 Analysis of Orbit Uncertainty Propagation Using Jet Transport 45 3.1 Executive Summary 45 3.2 Dynamical Models 47 3.2.1 Cartesian Dynamic Model 47 3.2.2 Cylindrical