Physics

This course, comprised of a lecture and discussion section, includes the following topics: 1) Introduction (historical notes, coordinate dependence of Newton‘s equations, systems with constraints); 2) Lagrange equations (systems w/o constraints, non-inertial reference frames, constraints and generalized coordinates, virtual displacements, D’Alembert’s principle, systems w/ constraints); 3) Hamilton‘s principle (variational calculus, derivation of Lagrange equations from Hamilton’s principle, Lagrange multipliers and constraints); 4) Symmetries and conservation laws (cyclic coordinates and canonical momenta, translational and rotational invariance, Noether theorem, translational invariance in time and energy conservation, energy conservation in 1D systems, Galilei invariance and Lagrangian of free particles, relativistic mechanics of free particles, gauge invariance, mechanical similarity); 5) Oscillations (coupled oscillators, driven oscillators, Green function of damped oscillator, parametric resonance, motion in rapidly oscillating fields); 6) Rigid bodies (degrees of freedom, tensor of inertia and kinetic energy, angular momentum, principal axes of tensor of inertia, equations of motion, Euler angles, free symmetric top, heavy symmetric top, fast top).

This six-week summer course provides individual research training through the experience of belonging to a specific laboratory at Tohoku University. Students are assigned to a laboratory research group with Japanese and international students under the supervision of Tohoku University faculty. They participate in various group activities, including seminars, for the purpose of training in research methods and developing teamwork skills. The specific topic studied depends on the instructor in charge of the laboratory to which each student is assigned. The methods of assessment vary with the student's project and laboratory instructor. Students submit an abstract concerning the results of their individual research each semester and present the results near the end of this program.