I just can’t understand how a rotation components can be written in terms of partial derivatives. Please throw some light on this, and also explain how we reached to the conclusion about orthogonality highlighted in the next para.
2026-03-07 15:12:41.1772896361
Confusion in $\mathbb{R}^3$ Rotations derivation
16 Views Asked by SHIKHAR CHAMOLI https://math.techqa.club/user/shikhar-chamoli/detail At
1
There are 1 best solutions below
Related Questions in COORDINATE-SYSTEMS
- How to change a rectangle's area based on it's 4 coordinates?
- How to find 2 points in line?
- Am I right or wrong in this absolute value?
- Properties of a eclipse on a rotated plane to see a perfect circle from the original plane view?
- inhomogeneous coordinates to homogeneous coordinates
- Find the distance of the point $(7,1)$ from the line $3x+4y=4$ measured parallel to the line $3x-5y+2=0.$
- A Problem Based on Ellipse
- Convert a vector in Lambert Conformal Conical Projection to Cartesian
- Archimedean spiral in cartesian coordinates
- How to find the area of the square $|ABCD|$?
Related Questions in VECTORS
- Proof that $\left(\vec a \times \vec b \right) \times \vec a = 0$ using index notation.
- Constrain coordinates of a point into a circle
- Why is the derivative of a vector in polar form the cross product?
- Why does AB+BC=AC when adding vectors?
- Prove if the following vectors are orthonormal set
- Stokes theorem integral, normal vector confusion
- Finding a unit vector that gives the maximum directional derivative of a vector field
- Given two non-diagonal points of a square, find the other 2 in closed form
- $dr$ in polar co-ordinates
- How to find reflection of $(a,b)$ along $y=x, y = -x$
Related Questions in GEOMETRY
- Point in, on or out of a circle
- Find all the triangles $ABC$ for which the perpendicular line to AB halves a line segment
- How to see line bundle on $\mathbb P^1$ intuitively?
- An underdetermined system derived for rotated coordinate system
- Asymptotes of hyperbola
- Finding the range of product of two distances.
- Constrain coordinates of a point into a circle
- Position of point with respect to hyperbola
- Length of Shadow from a lamp?
- Show that the asymptotes of an hyperbola are its tangents at infinity points
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?
Since $S$ rotates $x$ to $x'$ the transpose of $S$ rotates $x'$ back to $x$: $$ x_1=s_{11}x'_1+s_{21}x'_2+s_{31}x'_3 $$ and so on. It is easy to see that for example $s_{21}=\frac{\partial x_1}{\partial x'_2}$ and so on.