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.

Definition and overview of remote sensing, electromagnetic radiation and its interaction with matter, Spectral signatures of surface materials, physical basis of signatures, radiometric and geometric distortions and corrections, remote sensors and platforms – optical, infrared and microwave sensors, active remote sensing techniques: LIDAR and Microwave remote sensing, and radars, data formats, remote sensing data interpretation – visual and digital interpretation techniques, remote sensing applications.

Hypersonic air-breathing propulsion – overview of hypersonic propulsion research – challenges in system design – system performance and analysis – hypersonic intakes – supersonic combustors – expansion systems – engine cooling – liquid air-cycle engines – space plane applications – experimental and testing facilities – CFD applications and simulation exercises.

Introduction to microscale and nanoscale transport – basic phenomenon of conductive transport in nanoscale – basic aspects of quantum mechanics – basics of kinetic theory and statistical me- chanics – thermodynamic relations – Boltzmann transport equation – microscale heat conduction – basics of electron and phonon transport – thermal conductivity models – Equilibrium breakdown and characterisation of flow regimes in micro and nano scale – continuum approach – heat transfer in Poiseuille microflows – single phase convection in micro channels – rarefied gas flows – Slip models – Burnett and

Introduction to Turbomachines. Dimensional Analyses and Performance Laws.

Axial Flow Compressors and Fans: Introduction – aero-thermodynamics of flow through an axial flow compressor stage – losses in axial flow compressor stage – losses and blade performance estimation, radial equilibrium equation – design of compressor blades – 2-D blade section design, axial compressor characteristics – multi-staging of compressor characteristics – high Mach number compressor stages – stall and surge phenomenon – low speed ducted fans.

Elements of rocket propulsion – nozzle design, characteristic parameters, heterogeneous flow analysis – aerothermochemistry of combustion, dissociation, equilibrium composition, adiabatic temperature, and combustion product equilibrium flow nozzle expansion – elements of solid propellant system – internal ballistics and design of solid propellant – grain design and optimization – elements of liquid propulsion system – design and selection of injectors, combustion chambers, nozzle, cooling system, feed systems and tanks – combustion instability, low and high frequency instability and scaling