General features and applications of high temperature flows – Equilibrium Kinetic Theory: Maxwellian distribution, collision rates and mean free path – Chemical thermodynamics – Mixture of perfect gases, law of mass action – Statistical Mechanics: Enumeration of micro-states, energy distribution, contribution of internal structure – Equilibrium Flow: Ideal dissociating gas, equilibrium shock wave relations, nozzle flows – Vibrational and chemical rate processes – Flows with vibrational and chemical non-equilibrium.

Launch vehicle ascent trajectory design – Reentry trajectory design – Low thrust trajectory design – Satellite constellation design – Rendezvous mission design – Ballistic lunar and interplanetary trajectory design – Basics of optimal control theory – Mission design elements for various missions – Space flight trajectory optimization – Direct and indirect optimization techniques – Restricted 3-body problem – Lagrangian points – Mission design to Lagrangian point.

Problem formulation – Performance measures – Selection of performance measures – Dynamics programming – Optimal control law – Application to a routing problem – Recurrence relations – Computational procedures – Alternative approach through Hamiltonial-Jacobi-Bellman equation – Review of Calculus of Variations: Functionals involving several independent functions – Constrained minimization of functional – Optimal control: Variational approach – Necessary condition for opti- mal control – Pontryagin’s minimum principle – Additional necessary conditions – Minimum time problems – Optimal control

Principles of Inertial Navigation: Components, two-dimensional navigation – Coordinate systems – 3D strapdown navigation system – Strapdown system mechanizations – Attitude representation – Navigation equations expressed in component form – Effects of elliptic earth – Inertial Sensors: Gy- roscope principles, single-axis rate gyroscope, accelerometers, rate integrating gyroscope – Elements of guidance system – Guidance phases – Guidance trajectories – Guidance sensors – Classification of Guidance and Navigation Systems: Basic navigation systems, combined navigation systems – Clas- sificatio

Basic equations – Hierarchy of mathematical models – Mathematical nature of flow equations and boundary conditions – Finite difference and finite volume methods – Analysis of Schemes: Numerical errors, stability, numerical dissipation – Grid generation – Wave equation – Numerical Solution of Compressible Euler Equation: Discontinuities and entropy, mathematical properties of Euler equa- tion – Reconstruction-evolution – Upwind methods – Boundary conditions – Numerical solution of compressible Navier-Stokes equations – Turbulence Modeling: RANS, LES, DNS – Higher-order methods – Uncertainty

Introduction to turbulence – Equations of fluid motion – Statistical description of turbulent flows – Mean-flow equations – Space and time scales of turbulent motion – Jets, wakes and boundary layers – Coherent structures – Spectral dynamics – Homogeneous and isotropic turbulence – Two-dimensional turbulence – Coherent structures – Vorticity dynamics – Intermittency – Modeling of turbulent flows.

Introduction to Hypersonic Flows – Inviscid Hypersonic Flow: Newtonian flow, Mach number inde- pendence, Hypersonic similarity, Blast wave theory, Hypersonic small disturbance theory, Stagnation region flow – Viscous Hypersonic Flow: Similarity parameters, Self-similar solutions, Hypersonic tur- bulent boundary layer, Reference temperature method, Stagnation region flow field, Viscous interac- tions – Real Gas effects: Inviscid equilibrium and non-equilibrium flows, Viscous high temperature flows – Experimental facilities – Hypersonic design considerations.

Basics of acoustics – General theory of aerodynamic sound – Flow and acoustic interactions – Feed- back phenomenon – Supersonic jet noise – Sonic boom – Noise radiation from rotors and fans – Aeroacoustic measurements.

Concept of similarity and design of experiments – Measurement uncertainty – Design of subsonic, transonic, supersonic, hypersonic, and high enthalpy test facilities – Transducers and their response characteristics – Measurement of pressure, temperature, velocity, forces, moments, and dynamic sta- bility derivatives – Flow visualization techniques: Optical measurement techniques, refractive index based measurements, scattering based measurements – Data acquisition and signal conditioning – Signal and image processing.

Basic Experiments in Low Speed Wind Tunnels – Measurement of Aerodynamic Forces and Moments – Measurements of Pressure and Velocity – Flow Visualisation Techniques – Transient Flows: Shock Waves, Detonation – Experiments in Supersonic Flows – Optical Flow Visualisation Methods – Measurement of Flow Generated Sound.

Study of Pull Up - Pull Down Maneuver – Flight Simulator – Flight Controls of a Helicopter – Propeller Performance Testing – Measurement of Performance Parameters in Flight.