FYSA2021 Mechanics (4 cr)

• 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
  

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
  

Basic physics studies:

• FYSP1010 Introduction to Mechanics

• FYSP1020 Waves and thermodynamics

• 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. 

Lecture material in Finnish in TIM system