User:Subhash15/Trial 1

This is my user subpage for experimentation.

In Two-Dimensional Coordinate system first I would like to change vertical to south-north (bottom-top) and horizontal to west-east (left-right) I would also like to alter and add as follows normally to usually and z to z, normal to the xy plane at the origin O, vertical (down-up) orthogonal to both the x and y axes

Then I would add a caption to the image as shown below.

Fig 1

Additional Examples

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Fig 2

In Engineering Mechanics, it is quite common to use north-south (top-bottom) y axis, based on the logic that most load carrying structural elements, such as roof beams, bridge decks et al carry gravity forces directed from top to bottom causing deformations toward bottom; thus computing positively signed deflections in manual or automated analysis. Stephen Timoshenko uses this coordinate system in his books, Mechanics of Materials page 167, and Theory of Elasticity Fig. 26, page 41 and Fig. 28 page 46.

This changes the physical location of the quadrants, I, II, III, and IV. The first is now the south-east quadrant, and the order I to IV is clockwise. Note that in Fig. 2 positive x axis maps on to positive y axis by rotating 90° (smaller angle) clockwise about the normal to plane xy passing through origin O, while in Fig. 1 it is counterclockwise. Physical location of chosen point P also changes. Arctan${\frac {5}{3}}$ is the angle $\angle$XOP in both cases, taking care to measure it from positive x axis direction between 0 and $2\Pi$

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Fig 3

This figure is difficult to find in established text books. However,