FYSA2020 Mechanics (5 cr)

• 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) 

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 

• FYSP1010 Introduction to Mechanics

• FYSP1020 Waves and thermodynamics

• 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: 

• • Differential, partial derivative, gradient

  • 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. 

Luentomateriaali TIM:ssä