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e4dragon
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I have a test tomorrow and the book does not even explain it that well. Than You
What is orthogonal trajectory?
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- Orthogonal Trajectory
In summary, orthogonal trajectory refers to a set of curves that are perpendicular to another set of curves at every point of intersection. They are commonly used in mathematics, physics, and engineering to analyze and solve problems involving curves and surfaces. They are related to curves in that they are perpendicular to them, and have various applications in different fields such as solving differential equations and designing structures. The method of differentiation can be used to determine the orthogonal trajectory of a given curve.
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tiny-tim
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Welcome to PF!
Hi e4dragon! Welcome to PF!
For more detail, see http://en.wikipedia.org/wiki/Orthogonal_trajectory
Is there anything particular you don't understand about orthogonal trajectories?
Hi e4dragon! Welcome to PF!
"In mathematics, orthogonal trajectories are a family of curves in the plane that intersect a given family of curves at right angles."
For more detail, see http://en.wikipedia.org/wiki/Orthogonal_trajectory
Is there anything particular you don't understand about orthogonal trajectories?
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e4dragon
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i understand it now, sort of. thank you
1. What is the definition of orthogonal trajectory?
Orthogonal trajectory refers to a set of curves that intersect another set of curves at right angles (90 degrees) at every point of intersection. In other words, they are a family of curves that are perpendicular to each other.
2. Where are orthogonal trajectories commonly used?
Orthogonal trajectories are commonly used in mathematics and physics, particularly in the study of differential equations. They are also used in engineering and other branches of science to analyze and solve problems involving curves and surfaces.
3. How are orthogonal trajectories related to curves?
Orthogonal trajectories are related to curves in that they are a set of curves that are perpendicular to another set of curves. This means that at any point of intersection, the tangent lines of the two curves will be at right angles to each other.
4. What is the significance of orthogonal trajectories?
Orthogonal trajectories have several applications and significance in different fields. In mathematics, they can be used to solve differential equations and find solutions to various problems. In physics, they are used in the study of electric and magnetic fields. In engineering, they are used to design curved structures such as bridges and roads.
5. How can one determine the orthogonal trajectory of a given curve?
To determine the orthogonal trajectory of a given curve, one can use the method of differentiation. This involves finding the derivative of the given curve and then taking the negative reciprocal of the derivative to get the slope of the orthogonal trajectory at that point. This process is repeated for different points on the curve to obtain the entire orthogonal trajectory.
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