Frenet–Serret formulas - Wikipedia
网页In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space, or the geometric properties of the curve itself irrespective of any motion.
弗莱纳公式（Frenet–Serret formulas） - CSDN博客
网页2020年7月9日 · 弗莱纳公式（弗莱纳坐标系）在自动驾驶轨迹规划等领域应用广泛。. 单位切向量 T，单位法向量 N，单位副法向量 B，被称作弗莱纳标架（Frenet–Serret frame or TNB frame，他们的具体定义如下：T 是单位切向量，方向指向粒子运动的方向；N 是单位法向量 …
弗莱纳公式 - 维基百科，自由的百科全书
网页在向量微积分中，弗勒内-塞雷公式（Frenet–Serret 公式）用来描述欧几里得空间R 3 中的粒子在连续可微曲线上的运动。 更具体的说，弗勒内公式描述了曲线的 切向，法向，副法方向 之间的关系。
Frenet—Serret 标架 - 知乎 - 知乎专栏
网页\\ 以上四式合称Frenet—Serret 公式或者Frenet—Serret 运动方程 \text{Proof} 前面两式是定义，下面来证3、4式. 注意到 T,N,B 单位正交,从而 \dot{N}=<\dot{N},T>T+<\dot{N},N>N+<\dot{N},B>B. 根据分部积分的思想，我们有 <\dot{N},T>=\frac{d}{ds}<N,T>-<\dot{T},N>=0-\kappa<N,N>=-\kappa,
Joseph-Alfred Serret - Wikipedia
网页Joseph-Alfred Serret (French: [sɛʁɛ]; August 30, 1819 – March 2, 1885) was a French mathematician who was born in Paris, France, and died in Versailles, France.
Joseph Serret (1819 - 1885) - MacTutor History of Mathematics
网页Joseph Serret was a French mathematician best remembered for the Serret-Frenet formulas for a space-curve.
网页Contents. The Frenet–Serret frame of a space curve 1. The Frenet–Serret formulas 3. The first three derivatives of r 3. Examples and discussion 4. 4.1 The curvature of a circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.
2.4 Frenet-Serret formulae - MIT
网页The formulae (2.56) are known as the Frenet-Serret formulae and describe the motion of a moving trihedron along the curve. From these , , the shape of the curve can be determined apart from a translation and rotation. For arbitrary …
3.5: The Frenet-Serret Equations - Brown University
网页Using the equations for T'(t) and P'(t) it is fairly straightforward to show that c(t) = 0 and d(t) = s'(t)τ(t). This gives us three equations knowns as the Frenet-Serret Equations.
Frenet Formulas -- from Wolfram MathWorld
网页2024年8月22日 · Also known as the Serret-Frenet formulas, these vector differential equations relate inherent properties of a parametrized curve. In matrix form, they can be written where is the unit tangent vector , is the unit normal vector , is the unit binormal vector , is the torsion , is the curvature , and denotes .