Tutor in theoretical mechanics. Theoretical mechanics tutors

General course"Mechanics" is part of the course general physics. Students will get acquainted with the main mechanical phenomena and methods of their theoretical description. The lecture includes video recordings of physical demonstrations, studied mechanical phenomena.
The structure of the course is traditional. The course covers the classical material on the course of general physics, the section "Mechanics", read in the first year of the Faculty of Physics of Moscow State University in the first semester. The course will include the sections "Kinematics and dynamics of a material point and the simplest systems", "Conservation laws", "Motion of a material point in non-inertial frames of reference", "Fundamentals relativistic mechanics”, “Kinematics and dynamics solid body""Fundamentals of Mechanics of Deformable Media", "Fundamentals of Hydromechanics and Aeromechanics", " Mechanical vibrations and waves.
The course is aimed at bachelors specializing in natural sciences, as well as secondary school physics teachers and university professors. It will also be useful for schoolchildren who are deeply involved in physics.

Format

The form of education is part-time (distance).
Weekly classes will include watching thematic video lectures, including videos of lecture experiments and performing test items with automated verification of results. An important element learning discipline is independent decision physical tasks. The decision will have to contain strict and logically correct reasoning leading to the correct answer.

Requirements

The course is designed for bachelors of 1 year of study. Knowledge of physics and mathematics required high school(11 classes).

Course program

Introduction
B.1 Space and time in Newtonian mechanics
B.2 Frame of reference

Chapter 1. Kinematics and dynamics of the simplest systems
Clause 1.1. Kinematics of a material point and the simplest systems
Clause 1.2. Newton's laws
Clause 1.3. Laws that describe individual properties forces

Chapter 2 Conservation laws in the simplest systems
Clause 2.1. Law of conservation of momentum
Clause 2.2. mechanical energy
Clause 2.3. Connection of conservation laws with the homogeneity of space and time

Chapter 3 Non-inertial frames of reference
Clause 3.1. Non-inertial reference systems. Forces of inertia
Clause 3.2. The manifestation of the forces of inertia on the Earth
Clause 3.3. Principle of equivalence

Chapter 4 Fundamentals of relativistic mechanics
Clause 4.1. Space and time in the theory of relativity
Clause 4.2. Lorentz transformations
Clause 4.3. Consequences of the Lorentz transformations
Clause 4.4. Interval
Clause 4.5. Addition of speeds
Clause 4.6. Motion equation
Clause 4.7. Momentum, energy and mass in the theory of relativity

Chapter 5 Kinematics and dynamics of a rigid body
Clause 5.1. Rigid Body Kinematics
Clause 5.2. Rigid Body Dynamics
Clause 5.3. Kinetic energy of a rigid body
Clause 5.4. Gyroscopes, spinning tops

Chapter 6 Fundamentals of mechanics of deformable bodies
Clause 6.1. Deformations and stresses in solids
Clause 6.2. Poisson's ratio
Clause 6.3. Relationship between Young's modulus and shear modulus
Clause 6.4. Energy of elastic deformations

Chapter 7 fluctuations
Clause 7.1. Free vibrations systems with one degree of freedom
Clause 7.2. Forced vibrations
Clause 7.3. Addition of vibrations
Clause 7.4. Oscillations in coupled systems
Clause 7.5. Nonlinear vibrations
Clause 7.6. Parametric vibrations
Clause 7.7. Self-oscillations

Chapter 8 Waves
Clause 8.1. Propagation of an impulse in a medium. wave equation
Clause 8.2. Density and energy flux in a traveling wave. Umov vector
Clause 8.3. Reflection of waves, vibration modes
Clause 8.4. Elements of acoustics
Clause 8.5. shock waves

Chapter 9 Fundamentals of hydro and aeromechanics
Clause 9.1. Fundamentals of hydro- and aerostatics
Clause 9.2. Stationary flow of an incompressible fluid
Clause 9.3. Laminar and turbulent flow. Flow around bodies with liquid or gas

Learning Outcomes

As a result of mastering the discipline, the student must know the basic mechanical phenomena, methods of their theoretical description and methods of their use in physical devices; be able to solve problems from the "Mechanics" section of the general physics course.

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Analytic geometry Calculus of variations Vector Analysis +33 higher mathematics Geometry Discrete Math Differential geometry Differential Equations Combinatorics Linear algebra Linear geometry Linear programming Math statistics Mathematical physics Mathematical models Mathematical analysis Optimal decision methods Optimization methods Optimal Control Applied Mathematics Sopromat Tensor Analysis Theoretical mechanics Probability theory Graph theory Game theory Optimization theory Number theory Topology Trigonometry TFKT financial mathematics functional analysis Econometrics

Schoolchildren in grades 9-11 Students Adults

m. Dmitry Donskoy Boulevard

Maxim Alekseevich

Private teacher Experience 9 years

from 1 500 rub / hour

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Graduate of the mech-mat of Moscow State University. There is experience in the banking sector as an analyst, experience as a system analyst in the field of IT development. Knowledge Expand programming, relational databases (sql). First category in chess. There is a successful experience of working with all categories of students: Schoolchildren (OGE, Unified State Examination, improving academic performance) Students (almost all sections of higher mathematics and mechanics) Adults (classes "for oneself", help with work issues).

One lesson was held with Maxim, on the topic " tensor analysis". I would like to note the knowledge of the subject, as well as politeness and the ability to explain the topic well. All reviews (69)

OGE (GIA) USE school course Algebra Algebra of logic Analytic geometry Calculus of variations +32 Vector Analysis higher mathematics Computable functions Geometry Discrete Math Differential geometry Differential Equations Integral Equations Linear algebra Linear geometry Linear programming mathematical logic Math statistics Mathematical physics Mathematical models Mathematical analysis Optimal decision methods Optimization methods Optimal Control Applied Mathematics Sopromat Tensor Analysis Theoretical mechanics Probability theory Trigonometry TFKP Partial differential equations Equations of mathematical physics financial mathematics functional analysis Numerical Methods Econometrics

Schoolchildren 1-11 grades Students Adults

m. Sports

Igor Andreevich

School teacher Experience 11 years

from 1 400 rub / hour

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Theoretical mechanics tutor

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I have good experience in 1) preparation for the introductory Olympiads - students became winners of the Olympiads Lomonosov, "Phystech", "Kurchatov", Expand MOSH, Rosatom and Internet Physics Olympiads. 2) preparation for the Unified State Examination for high scores. In 2018, for example, I had three USE nicknames - one in mathematics, the second in computer science and the third in physics. As a result, for mathematics, the student received 76, and the rest both received 94. 3) in teaching children who from regular school enrolled in a strong school, in assistance for an in-depth program. I have several such students now. 4) in preparing students for various tests and exams - mainly electrical engineering, mechanics, physics and higher mathematics. In addition, I now work as an assistant at the Department of Informatics at the Moscow Institute of Physics and Technology (I conduct seminars on algorithms and data structures), as a physics teacher at the Intellectual school. mathematical school"Two by two". I work as a teacher of Olympiad programming at training camps at MIPT. I am studying for USE expert in physics and computer science this year.

good tutor. My son is preparing for the GIA. The subject is well explained. There are many examples. We are glad. All reviews (45)

OGE (GIA) USE preparation for the olympiads school course Algebra Analytic geometry Vector Analysis +22 higher mathematics Geometry Discrete Math Differential geometry Differential Equations Combinatorics Linear algebra Linear programming mathematical logic Mathematical physics Mathematical analysis Applied Mathematics Theoretical mechanics Probability theory Graph theory Number theory Trigonometry TFKT Partial differential equations Equations of mathematical physics functional analysis Numerical Methods

Schoolchildren in grades 5-11 Students Adults

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Yuri Nikolaevich

University teacher Experience 39 years

from 1 350 rub / hour

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Theoretical mechanics tutor

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Candidate of Physical and Mathematical Sciences.

My son started going to Yuri Nikolayevich's classes a couple of months ago. The teacher is very interesting, the teaching method is quite satisfactory. Plan to visit Expand all upcoming classes academic year, we hope to prepare well for the exam and further admission to the university. All reviews (39)

OGE (GIA) USE school course Algebra Analytic geometry Geometry Differential Equations +7 Linear algebra Math statistics Mathematical physics Mathematical analysis Theoretical mechanics Probability theory functional analysis

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m. Cherkizovskaya m. Shchelkovskaya

Khachatur Vardovich

Private teacher Experience 6 years

from 2 000 rub / hour

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Theoretical mechanics tutor

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My son is doing math. Khachatur Vardovich explains the material in an accessible and patient way, the child goes to classes with pleasure. In general, we are satisfied Expand result. Recomend for everybody! All reviews (8)

Schoolchildren in grades 9-11 Students Adults

m. Novokosino

Sergey Alekseevich

Student Experience 5 years

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Theoretical mechanics tutor

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Graduated from school with a gold medal. USE results: Russian language - 95, mathematics - 95, physics - 94, computer science Expand - 88. Winner and prize-winner municipal stage All-Russian Olympiad schoolchildren in Russian. Winner and prize-winner of the regional stage of the All-Russian Olympiad for schoolchildren in mathematics and physics Winner of the Olympiad "Conquer Sparrow Hills" in mathematics. Winner of the Olympiad "Phystech" in mathematics and physics. Winner of the Internet Olympiad for schoolchildren in physics. Winner of the Olympiad "Professor Zhukovsky" in physics. Winner of the municipal stage of the All-Russian Olympiad for Schoolchildren in Informatics. Taught mathematics in summer camps. Tutoring experience since 2014.

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determination of the level of knowledge
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Classes are divided into two parts: theoretical and practical. In theoretical lessons, the teacher will explain the material being studied, explaining the task. On the practical exercises solve problems in theoretical mechanics.

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Statics, dynamics and kinematics are combined into one discipline: the course of theoretical mechanics. A difficult subject to master will be easier to understand with a tutor in theoretical mechanics. On the portal " Highest mark» you can order in the regions and in Moscow.

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decide differential equations;

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The course deals with: the kinematics of a point and a rigid body (with different points view, it is proposed to consider the problem of orientation of a rigid body), classical problems of dynamics mechanical systems and rigid body dynamics, elements of celestial mechanics, motion of systems of variable composition, impact theory, differential equations of analytical dynamics.

The course covers all the traditional sections of theoretical mechanics, however Special attention given to consideration of the most informative and valuable for the theory and applications sections of dynamics and methods of analytical mechanics; statics is studied as a section of dynamics, and in the section of kinematics, the concepts necessary for the section of dynamics and the mathematical apparatus are introduced in detail.

Informational resources

Gantmakher F.R. Lectures on analytical mechanics. - 3rd ed. – M.: Fizmatlit, 2001.
Zhuravlev V.F. Fundamentals of theoretical mechanics. - 2nd ed. - M.: Fizmatlit, 2001; 3rd ed. – M.: Fizmatlit, 2008.
Markeev A.P. Theoretical mechanics. - Moscow - Izhevsk: Research Center "Regular and Chaotic Dynamics", 2007.

Requirements

The course is designed for students who own the apparatus of analytical geometry and linear algebra in the scope of the first-year program of a technical university.

Course program

1. Kinematics of a point
1.1. Problems of kinematics. Cartesian system coordinates. Decomposition of a vector in an orthonormal basis. Radius vector and point coordinates. Point speed and acceleration. Trajectory of movement.
1.2. Natural triangular. Expansion of velocity and acceleration in the axes of a natural trihedron (Huygens' theorem).
1.3. Curvilinear point coordinates, examples: polar, cylindrical and spherical coordinate systems. Velocity components and projections of acceleration on the axes of a curvilinear coordinate system.

2. Methods for specifying the orientation of a rigid body
2.1. Solid. Fixed and body-bound coordinate systems.
2.2. Orthogonal rotation matrices and their properties. Euler's finite turn theorem.
2.3. Active and passive points of view orthogonal transformation. Addition of turns.
2.4. Finite rotation angles: Euler angles and "airplane" angles. Expression of an orthogonal matrix in terms of finite rotation angles.

3. Spatial motion of a rigid body
3.1. Translational and rotational movement solid body. Angular speed and angular acceleration.
3.2. Distribution of velocities (Euler's formula) and accelerations (Rivals' formula) of points of a rigid body.
3.3. Kinematic invariants. Kinematic screw. Instant screw axle.

4. Plane-parallel motion
4.1. The concept of plane-parallel motion of the body. Angular velocity and angular acceleration in the case of plane-parallel motion. Instantaneous center of speed.

5. Complex motion of a point and a rigid body
5.1. Fixed and moving coordinate systems. Absolute, relative and figurative movement of a point.
5.2. Velocity addition theorem for complex movement points, relative and figurative speed points. The Coriolis theorem on the addition of accelerations for a complex motion of a point, relative, translational and Coriolis accelerations of a point.
5.3. Absolute, relative and portable angular velocity and angular acceleration of the body.

6. Motion of a rigid body with fixed point(quaternion presentation)
6.1. The concept of complex and hypercomplex numbers. Algebra of quaternions. Quaternion product. Conjugate and inverse quaternion, norm and modulus.
6.2. Trigonometric representation of the unit quaternion. Quaternion method of specifying body rotation. Euler's finite turn theorem.
6.3. Relationship between quaternion components in different bases. Addition of turns. Rodrigues-Hamilton parameters.

7. Exam work

8. Basic concepts of dynamics.
8.1 Momentum, angular momentum (kinetic moment), kinetic energy.
8.2 Power of forces, work of forces, potential and total energy.
8.3 Center of mass (center of inertia) of the system. The moment of inertia of the system about the axis.
8.4 Moments of inertia about parallel axes; the Huygens–Steiner theorem.
8.5 Tensor and ellipsoid of inertia. Principal axes of inertia. Properties of axial moments of inertia.
8.6 Calculation of angular momentum and kinetic energy body using the inertia tensor.

9. Basic theorems of dynamics in inertial and non-inertial frames of reference.
9.1 Theorem on the change in the momentum of the system in inertial system reference. The theorem on the motion of the center of mass.
9.2 Theorem on the change in the angular momentum of the system in an inertial frame of reference.
9.3 Theorem on the change in the kinetic energy of the system in an inertial frame of reference.
9.4 Potential, gyroscopic and dissipative forces.
9.5 Basic theorems of dynamics in non-inertial frames of reference.

10. Movement of a rigid body with a fixed point by inertia.
10.1 Dynamic Equations Euler.
10.2 Euler case, first integrals of dynamical equations; permanent rotations.
10.3 Interpretations of Poinsot and Macculag.
10.4 Regular precession in the case of dynamic symmetry of the body.

11. Motion of a heavy rigid body with a fixed point.
11.1 General formulation of the problem of the motion of a heavy rigid body around.
fixed point. Euler dynamic equations and their first integrals.
11.2 Qualitative Analysis motion of a rigid body in the Lagrange case.
11.3 Forced regular precession of a dynamically symmetric rigid body.
11.4 The basic formula of gyroscopy.
11.5 The concept of elementary theory gyroscopes.

12. Dynamics of a point in the central field.
12.1 Binet's equation.
12.2 Orbit equation. Kepler's laws.
12.3 The scattering problem.
12.4 The problem of two bodies. Equations of motion. Area integral, energy integral, Laplace integral.

13. Dynamics of systems of variable composition.
13.1 Basic concepts and theorems about changing the basic dynamic quantities in systems of variable composition.
13.2 Movement of a material point of variable mass.
13.3 Equations of motion of a body of variable composition.

14. Theory of impulsive movements.
14.1 Basic concepts and axioms of the theory of impulsive movements.
14.2 Theorems about changing the basic dynamic quantities during impulsive motion.
14.3 Impulsive motion of a rigid body.
14.4 Collision of two rigid bodies.
14.5 Carnot's theorems.

15. Test

Learning Outcomes

As a result of mastering the discipline, the student must:

Know:
- basic concepts and theorems of mechanics and the methods of studying the motion of mechanical systems arising from them;
Be able to:
- correctly formulate problems in terms of theoretical mechanics;
- develop mechanical and mathematical models that adequately reflect basic properties the phenomena under consideration;
- apply the acquired knowledge to solve relevant specific problems;
Own:
- decision skills classical problems theoretical mechanics and mathematics;
- the skills of studying the problems of mechanics and building mechanical and mathematical models that adequately describe a variety of mechanical phenomena;
- skills practical use methods and principles of theoretical mechanics in solving problems: force calculation, definitions kinematic characteristics bodies at various ways tasks of motion, determination of the law of motion of material bodies and mechanical systems under the action of forces;
- self-learning skills new information during production and scientific activity using modern educational and information technologies;