Learn · NPTEL

Course11110614469 lectures

Variational Calculus and its applications in Control Theory and Nanomechanics

Prof. Sarthok Sircar · IIIT Delhi

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Introduction / Euler Lagrange Equations - Part 1 Video
  2. Introduction / Euler Lagrange Equations - Part 2 Video
  3. Introduction / Euler Lagrange Equations - Part 3 Video
  4. Introduction / Euler Lagrange Equations - Part 4 Video
  5. Introduction / Euler Lagrange Equations - Part 5 Video
  6. Introduction / Euler Lagrange Equations - Part 6 Video

Week 2

  1. Special cases / Invariance, Existence and Uniqueness of solutions - Part 01 Video
  2. Special cases / Invariance, Existence and Uniqueness of solutions - Part 02 Video
  3. Special cases / Invariance, Existence and Uniqueness of solutions - Part 03 Video
  4. Special cases / Invariance, Existence and Uniqueness of solutions - Part 04 Video
  5. Special cases / Invariance, Existence and Uniqueness of solutions - Part 05 Video
  6. Special cases / Invariance, Existence and Uniqueness of solutions - Part 06 Video

Week 3

  1. Generalization / Numerical solution of Euler Lagrange Equations - Part 01 Video
  2. Generalization / Numerical solution of Euler Lagrange Equations - Part 02 Video
  3. Generalization / Numerical solution of Euler Lagrange Equations - Part 03 Video
  4. Generalization / Numerical solution of Euler Lagrange Equations - Part 04 Video
  5. Generalization / Numerical solution of Euler Lagrange Equations - Part 05 Video
  6. Generalization / Numerical solution of Euler Lagrange Equations - Part 06 Video

Week 4

  1. Isoperimetric Problems - Part 01 Video
  2. Isoperimetric Problems - Part 02 Video
  3. Isoperimetric Problems - Part 03 Video
  4. Isoperimetric Problems - Part 04 Video
  5. Isoperimetric Problems - Part 05 Video
  6. Isoperimetric Problems - Part 06 Video

Week 5

  1. "Problems with Holononomic and non- Holononomic Constraints, Variable Endpts - Part 01" Video
  2. "Problems with Holononomic and non- Holononomic Constraints, Variable Endpts - Part 02" Video
  3. "Problems with Holononomic and non- Holononomic Constraints, Variable Endpts - Part 03" Video
  4. Problems with Holononomic and non- Holononomic Constraints, Variable Endpts - Part 04 Video
  5. Problems with Holononomic and non- Holononomic Constraints, Variable Endpts - Part 05 Video
  6. Problems with Holononomic and non- Holononomic Constraints, Variable Endpts - Part 06 Video

Week 6

  1. Broken extremals / Hamiltonian Formulation - Part 01 Video
  2. Broken extremals / Hamiltonian Formulation - Part 02 Video
  3. Broken extremals / Hamiltonian Formulation - Part 03 Video
  4. Broken extremals / Hamiltonian Formulation - Part 04 Video
  5. Broken extremals / Hamiltonian Formulation - Part 05 Video
  6. Broken extremals / Hamiltonian Formulation - Part 06 Video

Week 7

  1. Hamilton-Jacobi Equations - Part 01 Video
  2. Hamilton-Jacobi Equations - Part 02 Video
  3. Hamilton-Jacobi Equations - Part 03 Video
  4. Hamilton-Jacobi Equations - Part 04 Video
  5. Hamilton's equations, Symplectic Maps, Hamilton-Jacobi Equations, Conservative systems, Video
  6. Hamilton-Jacobi Equations - Part 06 Video

Week 8

  1. Noether's Theorem / Introduction to Second Variation - Part 01 Video
  2. Noether's Theorem / Introduction to Second Variation - Part 02 Video
  3. Noether's Theorem / Introduction to Second Variation - Part 03 Video
  4. Noether's Theorem / Introduction to Second Variation - Part 04 Video
  5. Noether's Theorem / Introduction to Second Variation - Part 05 Video
  6. Noether's Theorem / Introduction to Second Variation - Part 06 Video

Week 9

  1. Conjugate points / Jacobi Accessory Equations / Introduction to Optimal Control Theory - Part 01 Video
  2. Conjugate points / Jacobi Accessory Equations / Introduction to Optimal Control Theory - Part 02 Video
  3. Conjugate points / Jacobi Accessory Equations / Introduction to Optimal Control Theory - Part 03 Video
  4. Conjugate points / Jacobi Accessory Equations / Introduction to Optimal Control Theory - Part 04 Video
  5. Conjugate points / Jacobi Accessory Equations / Introduction to Optimal Control Theory - Part 05 Video
  6. Conjugate points / Jacobi Accessory Equations / Introduction to Optimal Control Theory - Part 06 Video

Week 10

  1. Constrained Optimization in Optimal Control Theory - Part 01 Video
  2. Constrained Optimization in Optimal Control Theory - Part 02 Video
  3. Constrained Optimization in Optimal Control Theory - Part 03 Video
  4. Constrained Optimization in Optimal Control Theory - Part 04 Video
  5. Constrained Optimization in Optimal Control Theory - Part 05 Video
  6. Constrained Optimization in Optimal Control Theory - Part 06 Video

Week 11

  1. Introduction to Nanomechanics - Part 01 Video
  2. Introduction to Nanomechanics - Part 02 Video
  3. Introduction to Nanomechanics - Part 03 Video
  4. Introduction to Nanomechanics - Part 04 Video
  5. Introduction to Nanomechanics - Part 05 Video
  6. Introduction to Nanomechanics - Part 06 Video

Live Session

  1. Live Session 27-02-2021 Video
  2. Live Session 13-02-2022 Video
  3. Live Session 29-03-2022 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIIT Delhi
Department
Mathematics
Teacher
Prof. Sarthok Sircar
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
Who can watch
NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed