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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

Problem Solving AbilityKnowledge of physicsKnowledge of engineering

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.