http://www.foerstemann.name/dokuwiki/ 2012-05-20T22:24:41+02:00 http://www.foerstemann.name/dokuwiki/ http://www.foerstemann.name/dokuwiki/lib/tpl/default/images/favicon.ico text/html 2012-05-20T17:30:23+02:00 vaumann http://www.foerstemann.name/dokuwiki/doku.php/lectures:art07?rev=1337527823&do=diff Youtube video <http://www.youtube.com/watch?v=xOzVmC-4gpw> 0:00 Review of curvature 0:30 Curvature of surfaces (2-dim) 5:00 Bugs living in the surface: intrinsic (opposite: extrinsic) 6:00 Parallel transport, covariant deviation and geodesics are intrinsic 8:00 Gyroscopes represent physical parallel transport 9:30 Sign of curvature 11:30 Definition of curvature R = lim(dA->0) d theta / dA 12:00 Moving to 3 dimensions: an addition axis is needed … text/html 2012-05-18T15:05:39+02:00 vaumann http://www.foerstemann.name/dokuwiki/doku.php/lectures:start?rev=1337346339&do=diff Classical Mechanics Youtube playlist <http://www.youtube.com/playlist?list=PL189C0DCE90CB6D81> Lecture 1 Discrete systems, continuos physics: motion of a particle Lecture 2 Conservation of energy and momentum, principal of least action (part I) Lecture 3 Integration by parts, principal of least action (part II), examples Lecture 4 Radial potential, definition of variation, Noether theorem, Hamiltionian Lecture 5 Simple pendulum, double pendulum, harmonic oscillator, Hamiltonian form… text/html 2012-05-18T15:03:37+02:00 vaumann http://www.foerstemann.name/dokuwiki/doku.php/lectures:art06?rev=1337346217&do=diff Youtube video <http://www.youtube.com/watch?v=Pm5ROyoaMZA> 0:00 Space-time 1:00 Metric of space-time, proper time 2:30 In SRT the metric is constant 10:30 Accelerated frames of reference lead to curved coordinates 12:30 Equivalence principle: curved coordinates correspond to a gravitational field 14:00 Locally flat coordinates 14:30 Replacing a gravitational field by curved coordinates 17:30 Definition of flat space 20:00 Showing that it is alway… text/html 2012-05-13T15:53:34+02:00 vaumann http://www.foerstemann.name/dokuwiki/doku.php/lectures:art05?rev=1336917214&do=diff Youtube video <http://www.youtube.com/watch?v=WtPtxz3ef8U> 0:00 Tensor calculus 0:30 Done: tensor algebra 1:30 Why tensors are important 4:00 Values are coordinate dependent, equation are independent 6:00 Using A = B => A - B = 0 leads to 0 in every reference frame 10:00 Derivative of a tensor 10:30 Derivative of a scalar field phi(x) = const 14:00 Derivative of a vector field phi(x) = const 16:30 Use of curved coordinates leads to non-vanishin… text/html 2012-05-07T15:30:42+02:00 vaumann http://www.foerstemann.name/dokuwiki/doku.php/lectures:art04?rev=1336397442&do=diff Youtube video <http://www.youtube.com/watch?v=ttMI0dmmkrE> 0:30 Review of tensor algebra 1:30 Transformation rules of co- and contravaiant vectors 8:00 Displacements are contravariant, gradients are covariant 15:30 Transformation rules of rank-2-tensors 19:00 Showing that summing over upper and lower indices of a tensor gives a scalar 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