Description
Return a parametric arc-length integrand.
Differential-calculus formulas relate supplied local values and derivatives under explicit coordinate and unit conventions. A tangent term, curvature expression or directional derivative assumes the required differentiability and regularity; substituting numerical derivatives does not verify those hypotheses for an actual function.
Return a parametric arc-length integrand.
When to use this tool
Use Curve Arc Length Integrand when evaluating the stated local differential-calculus identity from supplied values.
How to use the tool and how it works
- Enter derivatives. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read integrand. Use the output convention below.
Return a parametric arc-length integrand. Require nonempty derivative vector; integrand = hypot(all coordinate derivatives).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| derivatives | Derivatives | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| integrand | Integrand | Required. Finite number. |
{
"input": {
"derivatives": [
3,
4
]
},
"output": {
"integrand": 5
}
}Limitations and assumptions
- This is speed in the supplied parameter units; no curve differentiation, regularity check or arc-length integral is performed.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- 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. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Differentiate or validate the complete function and its domain first; use suitable symbolic or numerical methods and check regularity and coordinate conventions for the intended interpretation.
References
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