Classical Mechanics: From Newtonian to Lagrangian Formulation
Develop your knowledge of the fundamental concepts and theories based on the classical mechanics in this course.
Online
12 Weeks
Free Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Course Overview
The ‘Classical Mechanics: From Newtonian to Lagrangian Formulation’ online certification course is developed for the students to study and discuss the classical concepts of mechanics in the domain of engineering and physics. This National Programme on Technology Enhanced Learning (NPTEL) free online training course is provided by Swayam initiated by the government of India. The classes of this core course of undergraduate level are conducted online for a period of twelve weeks.
The course instructor for this online program is Prof. Debalmalya Banerjee, faculty from the department of physics at the Indian Institute of Technology Kharagpur. This course helps the students develop their expertise and knowledge on concepts such as Newtonian laws and other theories of classical physics and gravity. This ‘Classical Mechanics: From Newtonian to Lagrangian Formulation’ online training program enables the students to get a certificate and credit points at the end of this All India Council for Technical Education approved course.
The Highlights
- Online mode
- Free training
- Twelve weeks
- Core program
- IIT faculty
- AICTE approved
- E-Certificate
- Credit points
Programme Offerings
- Online Classes
- Course Modules
- Lectures
- videos
- Weekly Assignments
- Final Exam
- course certificate
- Credit Points
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 1000 | yes | IIT Kharagpur |
The ‘Classical Mechanics: From Newtonian to Lagrangian Formulation’ certification fee refers to the registration fee for the certification exam.
Classical Mechanics: From Newtonian to Lagrangian Formulation fee structure :
Program Fee | Nil |
Exam Registration Fee | Rs 1000 |
Eligibility Criteria
Certificate qualifying details:
The students of the ‘Classical Mechanics: From Newtonian to Lagrangian Formulation’ certification by Swayam will receive the certificate after completing the course and assessments with at least 10/25 (25%) in the internal assessments, 30/75 (75%) in the final exam with a total average score of 40/100.
What you will learn
The ‘Classical Mechanics: From Newtonian to Lagrangian Formulation’ certification syllabus is structured for the students to understand the fundamental theories based on classical mechanics. The students of this course will get familiar with the concepts of Newtonian mechanics, rigid dynamics, and Lagrangian formulation of dynamics followed by small oscillations. By the end of this course, students will be equipped with mechanical knowledge and problem-solving skills.
Who it is for
The ‘Classical Mechanics: From Newtonian to Lagrangian Formulation’ online certification course is organized for the students and graduates of the field of engineering and physics.
Admission Details
The course registration for the ‘Classical Mechanics: From Newtonian to Lagrangian Formulation’ online course is done online through the course website.
Step 1: Find the course page using the following link,
https://onlinecourses.nptel.ac.in/noc21_ph32/preview
Step 2: Click on the ‘Sign-In/ Register’ option.
Step 3: Fill in the details and complete the registration.
Application Details
The applicants of the ‘Classical Mechanics: From Newtonian to Lagrangian Formulation’ certification course are required to enter their Swayam account details on the registration form or can sign in using their Google, Facebook, ad Microsoft account IDs.
The Syllabus
- Review of basic Newtonian mechanics
- kinematics problems
- A motion under resistance: terminal velocity
- System with variable mass: Rocket, raindrop, etc.
- Central forces: plane polar coordinate system
- 2-body central force problem
- General equation of the orbit
- Kepler’s laws of planetary motion
- The effective potential of a central force
- Escape velocity
- The eccentricity of the orbit under various initial conditions Satellite
- Ballistic missile
- Orbit transfer
- Moving coordinate system: pseudo forces
- Coriolis and centrifugal force
- Foucault’s pendulum
- Introduction to the system of particles
- Dynamics in center of mass frame
- Introduction to a rigid body
- Degrees of freedom (DOF) and constrains
- Rotational dynamics of a rigid body
- Moments of inertia tensor
- Principle moments of inertia
- Ellipsoid of inertia
- Parallel and perpendicular axis theorem
- Euler’s equation of rigid body rotation under external torque
- Torque free motion of spherical, symmetric, and asymmetric top
- Introduction to Euler angles, pitch, precession, and nutation
- The heavy symmetric top, the energy equation Special case of ‘fast’ and ‘sleeping’ top
- Lagrangian dynamics: Forces of constraining
- Virtual displacement
- Principle of the virtual wok and D’Alembert’s principle
- Generalized coordinates
- Lagrange’s equation of 1st kind
- Lagrange’s undetermined multiplier
- Generalized velocity and force
- Lagrange’s equation of 2nd kind
- Lagrangian, Classification of constrains
- Lagrange’s equations for non-holonomic systems
- Dissipation and gauge function
- The most general form of Lagrange’s equation
- Review of the rigid body including a heavy symmetric top
- Variation principle
- Calculus of variation
- Principle of least action, and Lagrange’s equation from its Application of variation principle (catenary, geodesic, etc.)
- Small oscillation: Introduction to coupled systems, normal modes
- Types of equilibrium
- Kinetic and potential energy of a coupled system
- Expression of energy in matrix form
- Equation of motion of a coupled system, normal frequencies, eigenvalues, and eigenvectors of K.E. and P.E. matrices,
- Diagonalization of K.E. and P.E. matrices
- Normal modes of oscillation
- Examples (linear molecules, spring-mass systems, etc.)
Evaluation process
- The students of this certification program will have to write the end-term proctored exam to receive the ‘Classical Mechanics: From Newtonian to Lagrangian Formulation’ certificate.
- The registration and payment for this final exam are done online through the course website and the exam is conducted from the select exam centers.
- The candidates will have to score a minimum of 30/75(75%) in this exam to qualify for the certification.
Instructors
IIT Kharagpur Frequently Asked Questions (FAQ's)
There are no mandatory prerequisites for this course.
The course is provided by the Swayam platform.
The program is conducted for twelve weeks.
Yes, this is a free learning program but the students should pay the registration fee for the certification exam.
You will get three credit points for this course.