Description
Check a supplied tangent/normal acceleration decomposition using an explicit absolute dot-product tolerance.
A mechanics calculation needs a coordinate frame, sign convention, and consistent force, length, mass, and time units. Vector projections, local balance terms, and ideal motion equations describe particular parts of a physical model. They do not automatically establish all equilibrium conditions or the validity of the model.
Check a supplied tangent/normal acceleration decomposition using an explicit absolute dot-product tolerance.
When to use this tool
Use Acceleration Tangent Normal Orthogonality when you need this particular projection, balance, frame conversion, or ideal-model component from supplied physical quantities.
How to use the tool and how it works
- Enter tangent, normal, tolerance. 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 dot, orthogonal. Inspect orthogonal before interpreting the associated values.
Require nonempty equally sized tangent and normal vectors and nonnegative tolerance. Return dot=sum(tangent[i]*normal[i]) and orthogonal=(abs(dot)<=tolerance).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| tangent | Tangent | Required. Array of finite number; maximum items 256. |
| normal | Normal | Required. Array of finite number; maximum items 256. |
| tolerance | Absolute dot-product tolerance in the product units of the two vectors. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| dot | Dot | Required. Finite number. |
| orthogonal | Orthogonal | Required. Boolean. |
{
"input": {
"tangent": [
1,
0
],
"normal": [
0,
2
],
"tolerance": 0
},
"output": {
"dot": 0,
"orthogonal": true
}
}Limitations and assumptions
- Tolerance uses the product unit of the vector components and is not an angle tolerance. Vectors need not be normalized or nonzero, so a zero vector passes without defining a tangent-normal frame.
- 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. Signed zero is exported as zero.
Alternative or Complementary methods
Use a complete force, motion, or energy model when a single contribution is insufficient. Check coordinate frames, idealizations, and dimensional consistency before combining calculated terms.
References
Similar or alternative tools
- Torque Axis Normalized Projection
Require three-component torque and axis arrays with nonzero axis norm; return axialTorque=dot(torque,axis)/norm(axis).
- Rotational Inertia Single Mass Contribution
Return the point-mass inertia contribution about a supplied nonzero axis through the origin.