Mathematics Exam > Mathematics Notes > Mathematics for IIT JAM, GATE, CSIR NET, UGC NET > Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences
Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET PDF Download
The starting point is the action, denoted 
(calligraphic S), of a physical system. It is defined as the integral of the Lagrangian L between two instants of time t1 and t2 - technically a functional of the N generalized coordinates q = (q1, q2, ... , qN) which define the configurationof the system:
where the dot denotes the time derivative, and t is time.
Mathematically the principle is[19][20][21]
where δ (Greek lowercase delta) means a small change. In words this reads:[18]
The path taken by the system between times t1 and t2 and configurations q1 and q2 is the one for which the action is stationary (no change) to first order.
In applications the statement and definition of action are taken together:[22]
The action and Lagrangian both contain the dynamics of the system for all times. The term "path" simply refers to a curve traced out by the system in terms of the coordinates in the configuration space, i.e. the curve q(t), parameterized by time (see also parametric equation for this concept).
The document Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET is a part of the Mathematics Course Mathematics for IIT JAM, GATE, CSIR NET, UGC NET.
All you need of Mathematics at this link: Mathematics
|
556 videos|198 docs
|
FAQs on Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences - Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
| 1. What is the principle of least action in classical mechanics? |  |
Ans. The principle of least action states that the path taken by a physical system between two points in space and time is the one that minimizes the action, which is a mathematical quantity defined as the integral of the Lagrangian over time. This principle is a fundamental principle in classical mechanics and provides a way to determine the equations of motion for a system.
| 2. How is the principle of least action related to the CSIR-NET Mathematical Sciences exam? | |
Ans. The principle of least action is a topic that is included in the syllabus of the CSIR-NET Mathematical Sciences exam. It is an important concept in classical mechanics and understanding it is crucial for solving problems related to the motion of particles and systems. Questions related to the principle of least action may be asked in the exam to test the candidate's understanding of this topic.
| 3. Can you explain the concept of action in classical mechanics? | |
Ans. In classical mechanics, action is a mathematical quantity that is defined as the integral of the Lagrangian over time. It represents the total effect of a system's motion between two points in space and time. The principle of least action states that the actual path taken by a system is the one that minimizes the action. By varying the path and finding the path that minimizes the action, we can determine the equations of motion for the system.
| 4. How is the principle of least action related to the Lagrangian formulation of classical mechanics? | |
Ans. The principle of least action is closely related to the Lagrangian formulation of classical mechanics. In this formulation, the Lagrangian is defined as the difference between the kinetic energy and the potential energy of a system. The equations of motion can then be derived by applying the principle of least action, which states that the path taken by a system is the one that minimizes the action, defined as the integral of the Lagrangian over time.
| 5. Can you provide an example of how the principle of least action is applied in classical mechanics? | |
Ans. Sure! Let's consider a simple example of a particle moving in one dimension under the influence of a gravitational force. The Lagrangian for this system would be the difference between the kinetic energy and the potential energy of the particle. By applying the principle of least action, we can vary the path taken by the particle and find the path that minimizes the action. This will give us the equation of motion for the particle, which is the second law of motion in this case.
Related Exams
About this Document
|
4.90/5 Rating |
|
Nov 22, 2024 Last updated |
Document Description: Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences for Mathematics 2024 is part of Mathematics for IIT JAM, GATE, CSIR NET, UGC NET preparation.
The notes and questions for Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences have been prepared according to the Mathematics exam syllabus. Information about Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences covers topics
like and Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences Example, for Mathematics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences.
Introduction of Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences in English is available as part of our Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
for Mathematics & Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences in Hindi for Mathematics for IIT JAM, GATE, CSIR NET, UGC NET course.
Download more important topics related with notes, lectures and mock test series for Mathematics
Exam by signing up for free. Mathematics: Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
Description
Full syllabus notes, lecture & questions for Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET - Mathematics | Plus excerises question with solution to help you revise complete syllabus for Mathematics for IIT JAM, GATE, CSIR NET, UGC NET | Best notes, free PDF download
Information about Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences
In this doc you can find the meaning of Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences defined & explained in the simplest way possible. Besides explaining types of
Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences theory, EduRev gives you an ample number of questions to practice Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences tests, examples and also practice Mathematics
tests
|
556 videos|198 docs
|
Download as PDF
|
Explore Courses for Mathematics exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
shortcuts and tricks
,video lectures
,Principle of least action - Classical Mechanics
,Viva Questions
,CSIR-NET Mathematical Sciences | Mathematics for IIT JAM
,Previous Year Questions with Solutions
,study material
,CSIR-NET Mathematical Sciences | Mathematics for IIT JAM
,Principle of least action - Classical Mechanics
,ppt
,Exam
,Important questions
,UGC NET
,CSIR NET
,CSIR NET
,CSIR NET
,GATE
,practice quizzes
,Principle of least action - Classical Mechanics
,Extra Questions
,past year papers
,UGC NET
,Semester Notes
,CSIR-NET Mathematical Sciences | Mathematics for IIT JAM
,GATE
,UGC NET
,Sample Paper
,mock tests for examination
,GATE
,Free
,MCQs
,Objective type Questions
,Summary
;
Additional Information about Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences for Mathematics Preparation
Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences Free PDF Download
The Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences is an invaluable resource that delves deep into the core of the Mathematics exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences now and kickstart your journey towards success in the Mathematics exam.
Importance of Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences
The importance of Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences cannot be overstated, especially for Mathematics aspirants.
This document holds the key to success in the Mathematics exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences Notes
Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences Notes on EduRev are your ultimate resource for success.
Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences Mathematics Questions
The "Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences Mathematics Questions" guide is a valuable resource for all aspiring students preparing for the
Mathematics exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences on the App
Students of Mathematics can study Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences is prepared as per the latest Mathematics syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup