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Figure1LeftBlurredmotioncapturedbyastaticcameraCenterThesamescenecapturedbyacamerawithaspeciallydesignedmotionthatcausesboththestaticanddynamicregionstobluridenticallyRightTheblurfromthecenterim. Standard 9. Person outside the bus. The . bus moved. away from the tree. The person is comparing the position of the bus with respect to the position of the tree. Reference (or origin) is position of the tree. Shengyang Dai . and. Ying Wu. EECS Department, Northwestern University. NORTHWESTERN. UNIVERSITY. http. ://vision.middlebury.edu/flow. /. Baker, . Scharstein. , Lewis, Roth, Black, Szeliski, . ICCV’07. Steven Lu. Overview. Significance of real-time motion blur rendering (Useful for what?). Slow performance of traditional methods. Some of the modern, more . efficient . methods . have problems, too. A new method is presented . Dan Hampton and Wolfgang Christian. Abstract. The double pendulum provides an ideal system in which to study chaotic motion. The system is relatively simple, but an infinitesimally small change in the initial conditions of the pendulum produces a drastically different trajectory for energies that exhibit chaotic motion. I use a phase-space plot, a Poincaré section, and a 3D trace to graphically represent the pendulum’s motion. The simulation allows for the initial energy and the masses on each pendulum to vary. The Feldberg eighth order numerical method serves as the algorithm for computing the motion. The program shows the energies at which the motion becomes chaotic while sometimes still exhibiting quasiperiodic trajectories, and it quantitatively demonstrates the unpredictability of this simple system. . AP Physics C. Mrs. Coyle. For pure rolling motion there is “rolling without slipping”, so at point P v. p. =0.. All points instantaneously rotate about the point of contact between the object and the surface (P).. Angular displacement, angular velocity, angular acceleration. Rotational energy. Moment of Inertia. Torque. Chapter 10:Rotation of a rigid object about a fixed axis. Reading assignment:. Chapter 10.1 to10.4, 10.5 (know concept of moment of inertia, don’t worry about integral calculation), 10.6 to . Exam on Monday. I’ll have a Mock exam to work on Friday. Solar Eclipse. Freds_excellent_eclipse.mpg. Solar Eclipses . Umbra. – region of total shadow. Penumbra. – region of partial shadow. Totality lasts only a few minutes!. Kinematics Terminology. Scalar vs. Vector. Scalar: . quantities that have only a size, but no direction. i. e. : . distance, speed. Vector: . quantities that have a size and direction. ie. : . displacement, velocity. Structure from motion. Given a set of corresponding points in two or more images, compute the camera parameters and the 3D point coordinates. Camera 1. Camera 2. Camera 3. R. 1. ,t. 1. R. 2. ,t. 2. R. Li Xu. 1. , . Jiaya. Jia. 1. , Yasuyuki Matsushita. 2. 1. The Chinese University of Hong Kong . 2. Microsoft Research Asia. Conventional Optical Flow. Middlebury Benchmark [Baker et al. 07]. Dominant Scheme: Coarse-to-Fine Warping. Given a set of corresponding points in two or more images, compute the camera parameters and the 3D point coordinates. Camera 1. Camera 2. Camera 3. R. 1. ,t. 1. R. 2. ,t. 2. R. 3. ,t. 3. ?. ?. ?. Slide credit: Noah . Examples:. Pendulum.. Oscillating spring (either horizontal or vertical) without friction.. Point on a wheel when viewed from above in plane of wheel.. Physics Classroom has a good lesson on simple harmonic motion under Waves, vibrations.. . Motion. Speed & Velocity. Acceleration. Newton’s First Law. Newton’s First Law of Motion. An object at rest will remain at rest and an object in motion will continue moving at a constant velocity unless acted upon by a net force.. Describing motion is occasionally difficult to do with words. Graphs can help simplify this description greatly. Position = Distance from a starting point. Velocity = rate of change in position. Acceleration = rate of change in velocity.