Description
Calculate the angle derivative of a Rodrigues rotation for a fixed supplied unit axis.
A vector is an ordered set of components in a chosen basis. Its norm measures magnitude, while dot products, projections, and coordinate transformations describe different relationships. Component order, angle units, normalization, and numerical tolerances determine the meaning of a computed result.
Calculate the angle derivative of a Rodrigues rotation for a fixed supplied unit axis.
When to use this tool
Use Vector Rodrigues Axis Angle Sensitivity when you need the particular coordinate operation, derivative, residual, or domain check under a known basis convention.
How to use the tool and how it works
- Enter vector, unitAxis, angle. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read derivative. Use the output convention below.
Require three-component vector and unitAxis with axis norm within 1e-12 of one. Differentiate the Rodrigues rotation expression with respect to angle: -vector*sin(angle)+(axis cross vector)*cos(angle)+axis*dot(vector,axis)*sin(angle).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| vector | Vector | Required. Array of Finite number.; maximum items 256. |
| unitAxis | Unit Axis | Required. Array of Finite number.; maximum items 256. |
| angle | Rotation angle in radians. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivative | Derivative with respect to the angle, per radian. | Required. Array of Finite number.; maximum items 256. |
{
"input": {
"vector": [
1,
0,
0
],
"unitAxis": [
0,
0,
1
],
"angle": 0
},
"output": {
"derivative": [
0,
1,
0
]
}
}Limitations and assumptions
- Angle is in radians and the result is a derivative per radian, not the rotated vector. The axis is assumed fixed; axis uncertainty and derivatives with respect to axis coordinates are not included.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Choose a complete vector or matrix operation when a single component or residual is insufficient. For sensitive near-zero or near-singular cases, inspect numerical conditioning and use an appropriate precision and tolerance.
References
Similar or alternative tools
- Vector Axis Angle Infinitesimal Step
Return the first-order active Rodrigues rotation v+angle*(unitAxis cross v), with angle in radians.
- Vector Angle Bisector Equal Norm Case
Normalize the sum of equal-norm vectors to obtain a bisector direction, rejecting a zero sum.