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carl123
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Find the curvature. r(t) = 9t i + 5 sin(t) j + 5 cos(t) k
MHB How to Find the Curvature of r(t)?
- Thread starter carl123
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- Curvature
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To find the curvature of the vector function r(t) = 9t i + 5 sin(t) j + 5 cos(t) k, the first step is to compute the first and second derivatives of r(t). The first derivative, r'(t), gives the velocity vector, while the second derivative, r''(t), provides the acceleration vector. The curvature can then be calculated using the formula κ(t) = |r'(t) × r''(t)| / |r'(t)|^3, where × denotes the cross product. Participants are encouraged to show their calculations for better assistance. Understanding these steps is crucial for accurately determining the curvature.