Find the orthogonal trajectories

Thread starter manal950
Start date Feb 22, 2013
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Orthogonal Trajectories

In summary, orthogonal trajectories are a set of curves that intersect another set of curves at right angles and have various applications in fields such as engineering and physics. To find them, you need to determine the gradient of the original curves and use the fact that the product of the gradients of two orthogonal curves is -1. They can only be found for certain types of curves and are important in the design of structures to ensure stability and efficiency.

Feb 22, 2013

manal950

Hi all

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Feb 22, 2013

HallsofIvy

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Start all over again! Each "[itex]\lambda[/itex]" gives a different member of the family of curves. To have an equation that describes the family and not an individual member, you have to elimininate [itex]\lambda[/itex]. That's the whole point of differentiating.

1. What are orthogonal trajectories?

Orthogonal trajectories are a set of curves that intersect another set of curves at right angles.

2. Why do we need to find orthogonal trajectories?

Finding orthogonal trajectories can be useful in various fields, such as engineering and physics, to solve problems involving intersecting curves.

3. How do you find orthogonal trajectories?

To find orthogonal trajectories, you need to first find the gradient of the original set of curves. Then, using the fact that the product of the gradients of two curves that are orthogonal is equal to -1, you can determine the equation for the orthogonal trajectories.

4. What is the significance of orthogonal trajectories?

Orthogonal trajectories have various applications, such as in the design of roads, bridges, and other structures, where intersecting curves need to be at right angles to ensure stability and efficiency.

5. Can orthogonal trajectories be found for any set of curves?

No, orthogonal trajectories can only be found for certain types of curves, such as circles, ellipses, and hyperbolas. They cannot be found for curves that do not have a smooth and continuous gradient.