I'm reading a book covering multiple topics in mathematics and physics. There's a chapter on tensors that had a very curious statement. It says "all curvilinear coordinate systems can relate to each other by some sort of rotation or series of rotations." I don't know what that precisely means. Does it mean that any curvilinear coordinate system can be transformed into any other one by rotations? It's not obvious to me that that is indeed the case. And if so, can we formally show that this is in fact the case? PS: The book is called Covariant Physics: From classical mechanics to general relativity and beyond.
2026-03-25 17:38:22.1774460302
Transformations of curvilinear coordinate systems
62 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in VECTOR-ANALYSIS
- Does curl vector influence the final destination of a particle?
- Gradient and Hessian of quadratic form
- Regular surfaces with boundary and $C^1$ domains
- Estimation of connected components
- Finding a unit vector that gives the maximum directional derivative of a vector field
- Gradient of transpose of a vector.
- Solve line integral
- Directional derivative: what is the relation between definition by limit and definition as dot product?
- Chain rule with intermediate vector function
- For which $g$ is $f(x)= g(||x||) \frac{x}{||x||}$ divergence free.
Related Questions in TENSORS
- Linear algebra - Property of an exterior form
- How to show that extension of linear connection commutes with contraction.
- tensor differential equation
- Decomposing an arbitrary rank tensor into components with symmetries
- What is this notation?
- Confusion about vector tensor dot product
- Generalization of chain rule to tensors
- Tensor rank as a first order formula
- $n$-dimensional quadratic equation $(Ax)x + Bx + c = 0$
- What's the best syntax for defining a matrix/tensor via its indices?
Related Questions in CURVILINEAR-COORDINATES
- On the relationship between the volume element in curvilinear coordinates and the Jacobian
- Why are these two ways of evaluating the curl of a vector field not actually equivalent?
- Given $\alpha(x,y,z) = \alpha_1\hat x +\alpha_2 \hat y+\alpha_3 \hat z$, how to write in the coordinates $\hat r, \hat \theta, \hat \phi$
- Dot product in spherical coordinates
- Expressing contravariant basis vectors in terms of position vector
- Find the center of mass in 3D
- Transform vectors from cartesian coordinates to curve coordinate system [2d]
- Coordinate and Non-coordinate basis (Orthonormality and Orthogonality)
- Scale factors in orthogonal coordinate systems
- Path on a sphere
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?