From the course: Complete Guide to Differential Equations Foundations for Data Science
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Orthogonal trajectories
From the course: Complete Guide to Differential Equations Foundations for Data Science
Orthogonal trajectories
- [Instructor] On to another differential equation application. This time you'll explore orthogonal trajectories. Let's begin by learning what orthogonal trajectories are. An orthogonal trajectory is a curve that intersects another curve at a 90-degree angle, also known as a right angle. Sometimes these are called perpendicular lines. Note that you can have a curve that intersects at more than one point on another curve. What's great is you can use differential equations to find orthogonal trajectories. When finding orthogonal trajectories using differential equations, it's more so a process you go through versus having one set formula that you use and solve like you would with other applications. Let's take a look at the steps. So with step one, you'll obtain the differential equation for the given family of curves; this may include getting the derivatives with respect to a variable such as x to find the slope of the curve. Step two, you'll find the negative reciprocal slope. In step…
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