# FYSA2020 Mechanics (5 cr)

Study level:
Intermediate studies
0-5
Language:
Finnish
Responsible organisation:
Department of Physics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023

## Description

• Newtonian mechanics (Newton’s laws and conservation laws)

• Oscillations (linear, damped, two-dimensional)

• calculus of variations (Euler-Lagrange equations)

• Lagrangian mechanics (Lagrangian, generalized coordinates, constraints, connection between conservation laws and symmetries, basics of Hamiltonian mechanics)

• gravitation and central-field motion (Newton’s law of gravitation, central-field motion, effective potential, planetary motion)

• Newtonian mechanics and selected types of problems

• non-intertial coordinate systems (rotating coordinate systems, centrifugal force and Coriolis force)

• rigid-body dynamics (energy and angular momentum, moments of inertia, principal axes, equations of motion for rotations, stability of rotations)

• coupled oscillations (general procedure of solving, applications)

• methods for solving various types of problems (lecture examples and problem sets)

## Learning outcomes

After completing the study unit the student can

• describe the foundations of Newtonian mechanics

• apply Newtonian mechanics in three-dimensional situations

• decide when Lagrangian or Hamiltonian mechanics is particularly useful

• apply Lagrangian mechanics in cases with constraints

• reduce for central forces a two-body problem into one-body problem

• describe planetary motion and the concept of constant of motion

• deduce the apparent forces in a rotating corrdinate system

• for the moment of inertia tensor for a rigid body

• apply the equations of motion of a rigid body

• find normal modes and their frequencies for coupled oscillations

• solve applied problems staring from the equations of the basic theory

## Description of prerequisites

Basic physics studies:
• FYSP1010 Introduction to Mechanics

• FYSP1020 Waves and thermodynamics

Selected topics from courses in mathematics:
• MATP211-213 Calculus 1-3, especially:

• Properties of elementary functions

• Derivative and integral

• MATA114 Differential equation; especially:

• 1st order separable differential equation

• 2st order constant-coefficient differential equation

• MATA181-181 Vector Calculus 1-2, especially:

• Integral over a three-dimensional volume

• Integral over a path

• MATP121-122 Linear Algebraand Geometry 1-2; especially

• Vectors: sum, dot product, cross product

• Matrix and determinant

• Products of vectors and matrices

• Rotation matrices

• Eigenvalues and eigenvectors

• In addition the basic properties of complex numbers.

## Study materials

Luentomateriaali TIM:ssä

## Literature

• Thornton & Marion: Classical dynamics of particles and systems. ISBN: 978-0-495-55610-7

## Completion methods

### Method 1

Description:
Ajankohta kevätlukukausi, 4. periodi
Evaluation criteria:
Harjoitukset 24/72, tentti 36/72 ja laboratoriotyöt 12/72.
Time of teaching:
Period 4
Select all marked parts

### Method 2

Description:
This completion method is intended for students for whom method 1 is not possible for specific reasons (e.g. language, living elsewhere). The course lecturer must be contacted before enrolling on the course.
Evaluation criteria:
Exam 60/72, laboratory work 12/72
Select all marked parts
Parts of the completion methods
x

### Teaching (5 cr)

Type:
Participation in teaching
0-5
Evaluation criteria:
Harjoitukset 24/72, tentti 36/72 ja laboratoriotyöt 12/72.
Language:
Finnish
Study methods:

x

### Independent study (5 cr)

Type:
Independent study