Description
Return osculating radius from speed and cross-product magnitude.
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 osculating radius from speed and cross-product magnitude.
When to use this tool
Use Parametric Curve Osculating Radius when evaluating the stated local differential-calculus identity from supplied values.
How to use the tool and how it works
- Enter speed, crossMagnitude. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read radius. Use the output convention below.
Return osculating radius from speed and cross-product magnitude. Require both positive; radius = speed³/crossMagnitude.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| speed | Speed | Required. Finite number; strictly above 0. |
| crossMagnitude | Cross Magnitude | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| radius | Positive curvature radius requiring nonzero speed and nonzero cross-product magnitude. | Required. Finite number. |
{
"input": {
"speed": 2,
"crossMagnitude": 4
},
"output": {
"radius": 2
}
}Limitations and assumptions
- Cross magnitude must be norm(r' cross r''); straight/zero-curvature and zero-speed cases are rejected rather than represented by an infinite radius.
- 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
Similar or alternative tools
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