FYSA2021 Mechanics (4 cr)

Study level:
Intermediate studies
Grading scale:
0-5
Language:
Finnish
Responsible organisation:
Department of Physics
Curriculum periods:
2024-2025, 2025-2026, 2026-2027, 2027-2028

Description

  • Newton's laws of motion and gravity, conservation laws
  • Oscillations: linear, damped, two-dimensional
  • Rotating coordinate system: centrifugal force and Coriolis force
  • Rotating body: moments of inertia, principal axes of inertia, equations of motion, stability
  • Lagrangian mechanics: Euler-Lagrange equations, generalized coordinates, constraints, symmetries
  • Two-body problem: constants of motion, planetary motion
  • Coupled oscillations: general method and practical applications
  • Generic methods of problem solving
  • Problem types in exercises

Learning outcomes

After completing the study unit the student

  • knows Newtons laws of motion and gravity and conservation laws
  • can apply Newtonian and Lagrangian mechanics
  • can apply the equations of motion of a rigid body
  • knows how to solve problems in non-inertial reference frames
  • knows how to treat the two-body problem and planetary motion
  • can determine normal modes and frequencies for coupled oscillators
  • solve problems using the various theoretical approaches of the course

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:

  1. Properties of elementary functions
  2. Derivative and integral
  • MATA114 Differential equation; especially:

  1. 1st order separable differential equation
  2. 2st order constant-coefficient differential equation
  • MATA181-181 Vector Calculus 1-2, especially:

  1. Differential, partial derivative, gradient
  2. Integral over a three-dimensional volume
  3. Integral over a path
  • MATP121-122 Linear Algebraand Geometry 1-2; especially

  1. Vectors: sum, dot product, cross product
  2. Matrix and determinant
  3. Products of vectors and matrices
  4. Rotation matrices
  5. Eigenvalues and eigenvectors
  • In addition the basic properties of complex numbers. 

Study materials

Lecture material in Finnish in TIM system

Literature

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

Completion methods

Method 1

Evaluation criteria:
Viikottaiset harjoitukset ja tentti.
Time of teaching:
Period 4
Select all marked parts

Method 2

Description:
Tämä suoritustapa on tarkoitettu opiskelijoille, joille toinen suoritustapa ei erityisistä syistä ole mahdollinen (esim. opetuskieli, asuminen muualla, suositus yksilöllisistä opintojärjestelyistä). Suoritustavasta on otettava yhteyttä opettajaan ennen kurssille ilmoittautumista.
Evaluation criteria:
Mahdolliset harjoitustehtävät sekä tentti.
Select all marked parts
Parts of the completion methods
x

Participation in teaching (4 cr)

Type:
Participation in teaching
Grading scale:
0-5

Teaching

x

Independent study (4 cr)

Type:
Independent study
Grading scale:
0-5
Language:
Finnish
Study methods:

Itsenäinen opiskelu, tentti ja laboratoriotyöt. 

Teaching