Фролов Михаил Владимирович

Offered By

Moscow Institute of Physics and Technology

Lectures on Selected Topics in Classical and Fluid Mechanics

Moscow Institute of Physics and Technology

About this Course

6,172 recent views

This course is devoted to selected problems of classical (theoretical) and fluid mechanics which are usually remain outside the standard course of mechanics. Despite the fact that the course is aimed at students with an understanding of the methods and approaches of classical and fluid mechanics, several lectures of the course are devoted to revision of material from the course of classical (theoretical) mechanics.
The course is aimed at an audience interested in theoretical physics methods for solving problems of classical and fluid mechanics.
The course is designed for an audience that has previously attended general course of classical and fluid mechanics and courses of higher mathematics:  mathematical analysis and differential equations theory.

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Intermediate Level

Approx. 10 hours to complete

English

Subtitles: English

Skills you will gain

Theoretical mechanicsclassical mechanicsAnalytical mechanics

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Intermediate Level

Approx. 10 hours to complete

English

Subtitles: English

Instructor

Фролов Михаил Владимирович

338 Learners

1 Course

Offered by

Moscow Institute of Physics and Technology

Московский физико-технический институт (Физтех) является одним из ведущих вузов страны и входит в основные рейтинги лучших университетов мира. Институт обладает не только богатой историей – основателями и профессорами института были Нобелевские лауреаты Пётр Капица, Лев Ландау и Николай Семенов – но и большой научно-исследовательской базой.

Основой образования в МФТИ является уникальная «система Физтеха», сформулированная Петром Капицей: кропотливый отбор одаренных и склонных к творческой работе абитуриентов; участие в обучении ведущих научных работников; индивидуальный подход к отдельным студентам с целью развития их творческих задатков; воспитание с первых шагов в атмосфере технических исследований и конструктивного творчества с использованием потенциала лучших лабораторий страны. Среди выпускников МФТИ — нобелевские лауреаты Андрей Гейм и Константин Новоселов, основатель компании ABBYY Давид Ян, один из авторов архитектурных принципов построения вычислительных комплексов Борис Бабаян и др.

Syllabus - What you will learn from this course

Week

Week 1

1 hour to complete

Introduction

The first week starts with the brief overview of the whole course, and continues with introduction to Lagrangian mechanics. We introduce the notion of constraints and discuss Lagrange equation of the first kind.

1 hour to complete

4 videos (Total 22 min), 3 readings, 1 quiz

4 videos

Promo56s

Overview3m

Constraints8m

Lagrange Equation of First Kind9m

3 readings

Overview10m

Additional Materials10m

Presentations, Bibliography10m

1 practice exercise

Test 130m

Week

Week 2

1 hour to complete

Lagrangian Formalism

The second week is devoted to Lagrange equation of the second kind. We formulate a concept of generalized coordinates, introduce Lagrange function and action function, analyze the role of the least action principle in mechanics and derive Lagrange equation of the second kind from it.

1 hour to complete

4 videos (Total 28 min), 1 reading, 1 quiz

4 videos

Lagrange Equation of the Second Kind. Generalized Coordinates.7m

Lagrange Equation of the Second Kind. Principle of the Least Action.6m

Properties of Lagrange Function4m

The Explicit Form of Lagrange Function9m

1 reading

Presentations10m

1 practice exercise

Test 230m

Week

Week 3

1 hour to complete

Lagrangian Formalism: Specific Problems

The third week continuous the study of Lagrangian formalism. We investigate the general features of an open system dynamics by solving Kelly’s problem. We also analyze the connection between the symmetry of Lagrangian function and the conservation lows for the basic physical quantities, and formulate the main issue of dynamics in central force field.

1 hour to complete

3 videos (Total 18 min), 1 reading, 1 quiz

3 videos

Conservation Laws and Symmetry of Lagrange Function6m

Kelly’s Problem7m

Dynamics in a Central Field3m

1 reading

Presentations10m

1 practice exercise

Test 330m

Week

Week 4

1 hour to complete

Scattering

The fourth week is devoted to scattering. We analyze general features of the scattering in the central field, and study the scattering on a solid sphere and Rutherford’s scattering. We also compare the main issues of the scattering for short-range and long-range potentials.

1 hour to complete

3 videos (Total 16 min), 1 reading, 1 quiz

3 videos

Scattering Cross Section5m

Scattering on a Solid Sphere4m

Rutherford’s Scattering6m

1 reading

Presentations10m

1 practice exercise

Test 430m

Week

Week 5

1 hour to complete

The theory of Oscillations

In the fifth week we investigate two interesting problems from the aria of oscillation theory: Kapitza pendulum and parametric resonance phenomenon.

1 hour to complete

3 videos (Total 22 min), 1 reading, 1 quiz

3 videos

Parametric Resonance7m

Motion in a Fast Oscillating Field7m

Kapitza pendulum6m

1 reading

Presentations10m

1 practice exercise

Test 530m

Week

Week 6

1 hour to complete

Elements of Solid Mechanics

In the sixth week we deal with the dynamics of an asymmetric rigid body and investigate an unusual Dzhanibekov effect (intermediate axis theorem).

1 hour to complete

2 videos (Total 12 min), 1 reading, 1 quiz

2 videos

Euler's Equations. Dzhanibekov Effect (Part 1)6m

Dzhanibekov Effect (Part 2)5m

1 reading

Presentations10m

1 practice exercise

Test 630m

Week

Week 7

1 hour to complete

Hamiltonian Formalism and Canonical Transformations

In the seventh week we proceed to the Hamiltonian formalism in classical mechanics. We introduce Hamilton function, form the system of Hamiltonian equations and establish the connection between Lagrangian and Hamiltonian mechanics. We also investigate the issues of canonical transformations.

1 hour to complete

2 videos (Total 9 min), 1 reading, 1 quiz

2 videos

Hamilton’s Equation4m

Сanonical Transformations5m

1 reading

Presentations10m

1 practice exercise

Test 730m

Week

Week 8

1 hour to complete

Hamilton–Jacobi Equation

In eighth week we introduce Hamilton-Jacobi equation and analyze the role of the action function in the framework of Hamiltonian mechanics. In this week we also summarize our study of the general methods and approaches in classical mechanics.

1 hour to complete

2 videos (Total 12 min), 1 reading, 1 quiz

2 videos

The Action as a Function of Coordinates and Time5m

Canonical Variables6m

1 reading

Presentations10m

1 practice exercise

Test 830m

Week

Week 9

1 hour to complete

Perturbation Theory

In the ninth week we investigate the perturbation theory in classical mechanics, which is based on the canonical transformation theory.

1 hour to complete

3 videos (Total 18 min), 1 reading, 1 quiz

3 videos

Perturbation Theory (Part 1)5m

Perturbation Theory (Part 2)5m

The Zoo of Classical Mechanics Equations6m

1 reading

Presentations10m

1 practice exercise

Test 930m

Week

Week 10

1 hour to complete

Elements of Fluid Mechanics

The last tenth week is devoted to selected problems of fluid mechanics, such as shock waves and nozzles.

1 hour to complete

3 videos (Total 19 min), 1 reading, 1 quiz

3 videos

Shock Waves (Part 1)5m

Shock Waves (Part 2)6m

Converging Nozzle6m

1 reading

Presentations10m

1 practice exercise

Test 1030m

Frequently Asked Questions

When will I have access to the lectures and assignments?
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
The course may not offer an audit option. You can try a Free Trial instead, or apply for Financial Aid.
The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
What will I get if I purchase the Certificate?
When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
Is financial aid available?
Yes, Coursera provides financial aid to learners who cannot afford the fee. Apply for it by clicking on the Financial Aid link beneath the "Enroll" button on the left. You’ll be prompted to complete an application and will be notified if you are approved. Learn more.

More questions? Visit the Learner Help Center.

Lectures on Selected Topics in Classical and Fluid Mechanics

Lectures on Selected Topics in Classical and Fluid Mechanics