Analytical mechanics

Physics 105. Spring 2018. Physics and Astronomy Department. Saint Mary's College of California

This course covers the principles of particle dynamics. Topics include rigid body dynamics, Lagrange’s equations, Hamilton’s principle, wave propagation, and normal modes of vibration in oscillating systems. Prerequisites: Physics 1-4 and Math 39.


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Instructor information

  • Office: Galileo 108A 925-631-4837
  • Office hours Tu 2:30-3:30 W 2:30-3:30 F 1:30-2:30
  • mrosario@stmarys-ca.edu

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Class information

Exam information

Other information, announcements

  • Project description (pdf).
  • Extra credit events. Pathways to Science lecture, SOS Career Panel, Informal conversation. Attend the event. Write one summary paragraph and one reflection paragraph. Submit it within one week of the event. (Max 2 extra credit events)
  • Other extra credit events: Math Senior Essays on the picture problem, gerrrymandering, and the hidden Markov model
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Class information

Recent announcements

  • Olowin Physics and Astronomy Lecture is March 12
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Calendar

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Date Text Topic Handouts, links, notes
M2.12 1.1 1.2 1.4 NEWTON'S 2ND LAW REVIEW. intro, vector review, Newton's second law, differential equations in-class problems, assignment
W2.142.12 1.1 1.2 1.4 intro, vector review, Newton's second law, differential equations
2.141.6 1.7 Cartesian and polar coordinates
F2.16 2.1 2.2 PROJECTILES AND CHARGED PARTICLES. air resistance, linear air resistance in-class problems
M2.192.16 2.1 2.2 air resistance, linear air resistance
2.192.4 2.5 quadratic air resistance, charged particle in B
W2.21 problems on air resistance in-class problems
F2.23 2.3 trajectory, range, Taylor series approx in-class problems
M2.26 1.5 3.1 3.2 MOMENTUM AND ANGULAR MOMENTUM. Newton's 3rd law, conservation of momentum, rockets in-class problems, assignment DUE 2.3 2.8 2.14 2.29 2.33 2.40 2.57
W2.28 3.3 3.4 center of mass, single particle angular momentum in-class problems, assignment
F3.02 3.4 Kepler's law, moment of inertia in-class problems
M3.05 4.1 ENERGY. kinetic energy, work-kinetic energy theorem DUE 2.37 2.14 2.20 3.3 3.9 3.1BC 3.17 3.33 3.31. in-class problems, assignment
W3.07 revisit what needs to be revisited: projectiles, momentum assignment
F3.09 4.2-4.4 potential energy, work-energy theorem assignment
M3.12 4.3 4.4 4.5 gradient of potential, curl of force, time dependent U assignment
W3.14 4.6 4.7 energy in 1D systems assignment due Fri
F3.16 exam review
M3.19 EXAM 1 review, grades, solutions, retake?
W3.21 5.1 5.2 OSCILLATIONS. Hooke's law. SHM solutions assignment due Fri
F3.23 5.2 SHM solutions cont'd assignment due Th4.05
SPRING BREAK
W4.04 5.4 damped oscillations. simulation in class problems. Due Thu.
F4.06 5.5 5.6 driven oscillations
M4.09 5.6 resonance, Q factor in class problems
W4.11 5.7 FOURIER SERIES. calculating the fourier series, even and odd functions
F4.13 5.7 Fourier coefficients, Fourier series solution to the driven oscillator
M4.16 6.1 6.3 CALCULUS OF VARIATIONS. statement of the problem, applying the Euler-Lagrange (E-L) equations
W4.18 6.2 6.3 deriving the E-L equation, more application of E-L equation probs due today 4/20
F4.20 NUMERICAL METHODS, PROJECT ASSIGNED. Project description and the Euler method
M4.23 7.1 LAGRANGE'S EQUATIONS. Hamilton's principle, Lagrangre's equations of motion. probs due today 4/20
W4.25 exam review Review sheet
F4.27 EXAM 2 Review sheet
2.21 problems on air resistance
2.23 2.3 trajectory, range, Taylor series approx
2.26 1.5 3.1 3.2 Newton's 3rd law, conservation of momentum, rockets
2.28 3.3 3.4 center of mass, angular momentum
3.02
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