Cylindrical and Polar Coordinate Systems Chapter 13.7.

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Presentation transcript:

Cylindrical and Polar Coordinate Systems Chapter 13.7

Motivating question… What is the shortest route you could fly from Edmonton to Amsterdam? What is the shortest route you could fly from Edmonton to Amsterdam? Edmonton (53.5N, 113.5W)Edmonton (53.5N, 113.5W) Amsterdam (52.7 N, 5.7 E)Amsterdam (52.7 N, 5.7 E) …link to Maple worksheet on visualizing plots in cylindrical and spherical polar coordinate systems

Spherical Polar Coordinates

Going to Amsterdam… This is the “fly straight east” path This is the “great circle” path

Fly “Straight East” Trip distance is the fraction of a circle of this radius one flies when going from Edmonton to Amsterdam. This is easy because the two cities are almost the same latitude. Edmonton (53.5N, 113.5W) Amsterdam (52.7 N, 5.7 E) Is this the shortest path?

The Geodesic Path… The shortest path is part of a great circle (one centered on the center of the earth). This is also known as a geodesic path All we need is a mathematical technique to find the angle between two vectors … hmm …

Spherical Polars to Cartesians Edmonton (53.5N, 113.5W) Amsterdam (52.7 N, 5.7 E) Edmonton Amsterdam