I would like to know what is the name of the derivative of the curvature of a plane curve. It should be called "sharpness", but I cannot find a reference. There should also be a connection with the jerk. I have the same question for the second derivative of the curvature, which has a connection with the snap. These topics are involved in the $G^4$ interpolation with splines. Thanks.
2026-03-31 22:08:28.1774994908
Derivatives of the curvature of a plane curve
1.2k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in DIFFERENTIAL-GEOMETRY
- Smooth Principal Bundle from continuous transition functions?
- Compute Thom and Euler class
- Holonomy bundle is a covering space
- Alternative definition for characteristic foliation of a surface
- Studying regular space curves when restricted to two differentiable functions
- What kind of curvature does a cylinder have?
- A new type of curvature multivector for surfaces?
- Regular surfaces with boundary and $C^1$ domains
- Show that two isometries induce the same linear mapping
- geodesic of infinite length without self-intersections
Related Questions in REFERENCE-REQUEST
- Best book to study Lie group theory
- Alternative definition for characteristic foliation of a surface
- Transition from theory of PDEs to applied analysis and industrial problems and models with PDEs
- Random variables in integrals, how to analyze?
- Abstract Algebra Preparation
- Definition of matrix valued smooth function
- CLT for Martingales
- Almost locality of cubic spline interpolation
- Identify sequences from OEIS or the literature, or find examples of odd integers $n\geq 1$ satisfying these equations related to odd perfect numbers
- property of Lebesgue measure involving small intervals
Related Questions in PLANE-CURVES
- Finding a quartic with some prescribed multiplicities
- How to use homogeneous coordinates and the projective plane to study the intersection of two lines
- Suggest parametric equations for a given curve
- Interpolation method that gives the least arc lenght of the curve.
- Tangent plane when gradient is zero
- Show this curve is a closed set in $R^2$ by using the definition
- Let $F(X,Y,Z)=5X^2+3Y^2+8Z^2+6(YZ+ZX+XY)$. Find $(a,b,c) \in \mathbb{Z}^3$ not all divisible by $13$, such that $F(a,b,c)\equiv 0 \pmod{13^2}$.
- Find the equation of the plane which bisects the pair of planes $2x-3y+6z+2=0$ and $2x+y-2z=4$ at acute angles.
- Could anyone suggest me some good references on interpolation that include other mathematical structures than just single variable functions?
- Question on the span of a tangent plane
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Different terms are used in different fields.
I have often heard car stylists refer to the "acceleration" of a curve, by which they mean the rate at which the curvature (or radius of curvature) is changing. When they say a curve has "a lot of acceleration", they mean that there is a large change in curvature over the length of the curve, which in turn means that the rate of change of curvature must be large.
They never say whether they are thinking of the rate of change of curvature with respect to arclength or some other parameter. Of course, arclength is the only parameter that makes much physical sense.
In physics, dynamics, and design of machinery, roads, and railway tracks, rate of change of acceleration is called "jerk". Since acceleration is closely related to curvature (especially when a curve is being traversed at constant speed), jerk is related to the derivative of curvature. In the design of railway tracks, people use special transition curves to avoid discontinuities of curvature.
For some related material, please see my answer to this other question.