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Theoretical Classical Mechanics: From Beginner to Expert

Theoretical Classical Mechanics: From Beginner to Expert

Loại khoá học: Science

Theory & Examples: Kinematics, Dynamics, Differential Equations (Including Maths & Python3), Lagrangian & Hamiltonian

50.000 VND

90 VND

Đầy Đủ Bài Giảng

Học Online Tiện Lợi

Kích Hoạt Nhanh 2-5 Phút

Thanh toán tự động

Được phép tải xuống

Mô tả

This course is for everyone who wants to learn about classical mechanic: Beginners to experts!

A bit of college mathematics (basic derivatives, integrals & vectors) is all you need to know!

Classical mechanics is the foundation of all disciplines in physics. It is typically at the very beginning of the university-level physics education. But that does not mean the classical physics is always super easy or even boring. Things become extremely complicated quickly and can lead to unexpected solutions. We can describe classical mechanics on different levels. I can guarantee that you will learn a lot no matter what your current skill level is.

You are kindly invited to join this carefully prepared course in which we derive the following concepts from scratch. I will present examples and have prepared quizzes and exercises for all topics.

[Level 1] Beginner: Kinematics (3 hours)

Overview & mathematical basics (derivatives, integrals, vectors)
Kinematics: Position, velocity & acceleration

[Level 2] Intermediate: Dynamics (9 hours)

Mathematics (Coordinate systems, multidimensional derivatives & integrals)
Dynamics: Forces & related quantities (work, potentials, energy, momentum)
Dynamics of the circular motion (torque, angular momentum)

[Level 3] Advanced: Theoretical mechanics (3.5 hours)

Lagrange’s approach (Constraints, action, Noether's theorem)
Hamilton’s approach & beyond (Legendre transformation, Hamilton's equations of motion)

[Level 4] Expert: Differential equations (8 hours)

Advanced mathematics (Complex numbers & matrices)
Differential equations: Analytical solution
Numerical solution with Python3

Why me?

My name is Börge Göbel and I am a postdoc working as a scientist in theoretical physics. Therefore, I use theoretical classical mechanics very often but I have not forgotten the time when I learned about it and still remember the problems that I and other students had.
I have refined my advisor skills as a tutor of Bachelor, Master and PhD students in theoretical physics and have other successful courses here on Udemy.

I hope you are excited and I kindly welcome you to our course!

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Yêu cầu

Nội dung khoá học

12 sections

[Level 1] Overview & Mathematical basics

5 lectures

Structure of this course

04:35

About the following videos

00:06

[Mathematical Basics] Derivatives

12:59

[Mathematical Basics] Integrals

06:51

[Mathematical Basics] Vectors

19:51

Kinematics

22 lectures

Section intro

00:37

Kinematics overview

05:44

Uniform motion in one dimension

03:33

Definition of velocity and acceleration

11:47

Derivatives and integrals in kinematics

10:00

Example: Derivatives and integrals in kinematics

08:12

Motion with constant acceleration

03:12

Superposition principle: Throw in multiple dimensions

11:15

About exercises and quizzes

00:49

Test your knowledge!

7 questions

[Exercise] Acceleration in a roller coaster

02:59

[Solution] Acceleration in a roller coaster

05:34

Circular motion

07:18

Uniform circular motion: Constant angular velocity

05:28

Constant angular acceleration

04:23

Difficult example: Pendulum, swing & carousel

09:38

Simplified example: Harmonic oscillator

08:29

Test your knowledge!

5 questions

[Exercise] Roundabout, carousel, merry-go-round

02:00

[Solution] Roundabout, carousel, merry-go-round

05:22

Section outro

00:43

Slides of this section

00:05

[Level 2] More mathematical basics

14 lectures

Section intro

01:19

Explanation: Please read before starting with this section!

00:30

Differentiation: From derivatives in 1D to partial and directional derivatives

12:45

Multidimensional derivatives: Nabla operator, gradient, curl and divergence

26:54

Test your knowledge about the Nabla operator.

6 questions

[Exercise] 3-dimensional derivatives

00:07

[Solutions] 3-dimensional derivatives

15:33

Integration: From 1D to multidimensional integrals

17:49

Line integrals

11:00

Alternative coordinate systems

13:50

Integration in spherical coordinates

14:48

Taylor expansion

10:42

Section outro

00:21

Slides of this section

00:05

Dynamics: Newton's approach

27 lectures

Section intro

01:07

Mass, Inertia & Forces

08:39

Newton's axioms

04:26

Weight & Gravity

14:41

Pulley

07:49

Forces of an inclined plane

04:54

Pendulum & Harmonic oscillator

10:00

Friction forces

11:15

Test your knowledge!

7 questions

[Exercise] Forces: Inclined plane and friction

02:50

[Solution] Forces: Inclined plane and friction

07:47

Conservative forces & Potentials

10:36

Work & Relation to potentials

14:21

Work of pulleys

05:14

Energy & Energy conservation

14:46

Power

05:47

Test your knowledge!

7 questions

[Exercise] Energy: Spaceship

04:46

[Solution] Energy: Spaceship

20:24

Momentum & Momentum conservation

05:15

Inelastic collisions

09:43

Elastic collisions

12:07

Test your knowledge!

4 questions

[Exercise] Collision analysis

03:25

[Solution] Collision analysis

10:55

Section outro

00:42

Slides of this section

00:05

Dynamics of the circular motion

30 lectures

Section intro

01:19

Centripetal force

15:10

Centripetal versus centrifugal force

02:38

Work of centripetal force

01:54

Test your knowledge!

3 questions

[Exercise] Roller coaster

03:45

[Solution] Roller coaster

19:56

Rotational energy

05:32

Moment of inertia

09:59

Moment of inertia: Stick

06:30

Moment of inertia: Sphere

11:50

Test your knowledge!

3 questions

[Exercise] Rolling objects

02:34

[Solution] Rolling objects

10:46

Torque

05:35

Levers

04:17

Angular momentum & Angular momentum conservation

10:27

Test your knowledge!

4 questions

[Exercise] Torque & Angular momentum

05:17

[Solution] Torque & Angular momentum

11:36

Comparison: Translation versus rotation

05:40

Spinning top: Rotation, precession & nutation

15:16

Inertial versus accelerated frame of reference: Velocity

11:16

Inertial versus accelerated frame of reference: Forces

14:46

Coriolis force

07:19

Motion of planets: Kepler’s 1st law

17:07

Motion of planets: Kepler’s 2nd law

06:00

Motion of planets: Kepler’s 3rd law

05:58

Section outro

01:00

Slides of this section

00:05

[Level 3] Theoretical mechanics: Lagrange's approach

27 lectures

Section intro

01:46

Constraints

08:09

D'Alembert's principle

03:43

D’Alembert’s principle: Generalized coordinates & Example: Pendulum

14:38

[Exercise] D'Alembert's principle: Inclined plane

03:44

[Solution] D'Alembert's principle: Inclined plane

05:31

Generalized forces

03:39

Lagrange equation

09:16

Euler-Lagrange equation (2nd kind)

04:17

Euler-Lagrange equation: Harmonic oscillator

03:44

[Exercise] Lagrangian mechanics: Pendulum & Kepler problem

05:16

[Solution] Lagrangian mechanics: Pendulum

04:53

[Solution] Lagrangian mechanics: Kepler problem

09:24

Test your knowledge about Lagrangian mechanics

6 questions

Lagrangian & Action

03:49

Hamilton’s principle of stationary action

09:28

Euler-Lagrange equation derived from Hamilton's principle

06:42

Why is Hamilton’s principle true? - Example: Vertical throw

07:17

Mathematical detour on action: Calculus of variations

07:27

Euler-Lagrange equation (1st kind)

02:04

Euler-Lagrange equation: Atwood's machine

11:31

Noether theorem

06:33

Noether theorem: Rotation invariance & Angular momentum

04:33

Noether theorem: Time invariance & Hamiltonian

06:32

Test your knowledge about Lagrangian mechanics

5 questions

Section outro

00:34

Slides of this section

00:05

Theoretical mechanics: Hamilton's approach & beyond

13 lectures

Section intro

00:55

Hamiltonian

03:18

Mathematical detail: Legendre transformation

10:20

Hamilton’s equations of motion

05:24

Phase space & Example: Harmonic oscillator

06:53

[Exercise] Hamiltonian mechanics: Pendulum & Kepler problem

04:12

[Solution] Hamiltonian mechanics: Pendulum

05:32

[Exercise] Hamiltonian mechanics: Kepler problem

09:22

Time evolution & Poisson bracket

04:13

Hamilton-Jacobi equation & Alternative formulations of classical mechanics

07:16

Test your knowledge about Hamiltonian mechanics!

3 questions

Section outro

00:34

Slides of this section

00:05

[Level 4] Advanced mathematical basics

16 lectures

Section intro

01:28

Explanation: Please read before starting with this section!

00:25

Complex numbers 1 - What are complex numbers?

09:25

Complex numbers 2 - Addition, subtraction & Complex plane

13:08

Complex numbers 3 - Multiplication & division

09:37

Complex numbers 4 - Exponentials & Polar representation

19:43

[Exercise] Complex numbers

00:07

[Solution] Complex numbers

14:10

Test your knowledge about complex numbers.

9 questions

Matrices 1 - What is a matrix?

10:16

Matrices 2 - Matrix addition & subtraction

02:11

Matrices 3 - Matrix multiplication

13:54

Matrices 4 - Calculating the determinant of a matrix

14:44

Matrices 5 - Eigensystems: Eigenvalues & Eigenvectors of a matrix

18:44

[Exercise] Matrices

Processing..

[Solution] Matrices

14:49

Differential equations: Analytical methods and simple examples from physics

19 lectures

Section intro

01:47

What are differential equations? Motivation & Example

12:59

Classification of differential equations

04:58

Classification of ordinary differential equations (ODE)

06:26

Trivial case: Direct integration

03:48

Example: Free fall

02:37

Homogeneous linear differential equations & Exponential ansatz

12:25

Example of exponential ansatz: Harmonic oscillator

09:15

[Exercise] Homogeneous differential equations

Processing..

[Solution] Homogeneous differential equations

11:05

[Exercise] Damped harmonic oscillator

Processing..

[Solution] Damped harmonic oscillator

17:26

Inhomogeneous linear differential equations

03:32

Example: Driven harmonic oscillator

04:07

[Exercise] Inomogeneous differential equation

Processing..

[Solution] Inomogeneous differential equation

07:42

How to continue

02:50

Section outro

00:32

Slides of this section

00:05

Differential equations: Solving advanced physics problems numerically [Python]

25 lectures

Section intro

02:00

[How to] Download and install Python3 & Jupyter Notebook

08:43

Download the template file

00:05

Background: Euler method

15:13

Example 1: Radioactive decay solved with a function

07:26

Example 2: Free fall - Higher-order differential equations

12:43

Example 3: Pendulum as a harmonic oscillator

07:10

Accurate solution of the pendulum

05:05

Adding damping and driving forces

06:55

Improvement: Use the SciPy function solve_ivp

08:05

Example 4: Simulating a rolling ball - Two decoupled oscillators

14:21

Download the final notebook

00:01

Rolling ball in Wolfram Mathematica

07:33

Download the template file

00:05

3-body problem 1/5: Coupled differential equations for sun, earth & moon

06:22

3-body problem 2/5: Coding the differential equations for sun, earth & moon

12:23

3-body problem 3/5: Solving the differential equations for sun, earth & moon

06:27

3-body problem 4/5: Analyzing the orbital motion of earth & moon

13:13

3-body problem 5/5: Comment on inclination of the moon

01:52

Spaceship 1/5: Coding & Solving the differential equations

08:57

Spaceship 2/5: Changing starting velocity: Elliptical orbit around earth

06:59

Spaceship 3/5: Simulating earth escape

08:54

Spaceship 4/5: Simulating a moon encounter

05:17

Spaceship 5/5: Brake maneuver to reach moon orbit

15:47

Download the final notebook

00:03

Coupled oscillators: Differential equation, Eigensystem & Fourier analysis

10 lectures

Section intro

01:45

Download the template file

00:05

Three coupled oscillators: Equations of motion

06:09

Numerical solution of the coupled differential equations

10:38

Analytical solution: Determining the Eigensystem

09:42

Recovering the eigenfrequencies by Fourier transform

13:07

Fitting the numerical solution with harmonic functions

15:34

Download the final notebook

00:03

Section outro

00:48

THANK YOU & GOODBYE!

00:56

[Outlook] Chaos

8 lectures

Section intro

00:51

Download the template file

00:05

Lorenz systems - Explanation of the differential equation

03:03

Solving the Lorenz differential equation for the chaotic case

13:15

Solving the Lorenz differential equation for the non-chaotic case

03:36

Download the final notebook

00:03

Section outro

00:16

Congratulations! Bonus Content!

00:32

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