Description
Project a supplied three-component angular momentum onto a declared axis; a zero momentum has no directional share.
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.
Project a supplied three-component angular momentum onto a declared axis; a zero momentum has no directional share.
When to use this tool
Use Angular Momentum Axis Share 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 angularMomentum, axis. 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 projection, magnitude, signedShare, defined. Inspect defined before interpreting the associated values.
Require three-component angularMomentum and a nonzero three-component axis. Compute magnitude with hypot and signedShare from the normalized dot-product operation, then projection=magnitude*signedShare. A zero angularMomentum returns projection=0, magnitude=0, signedShare=0, and defined=false.1
The normalized dot-product operation supplies the directional cosine used by this projection.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| angularMomentum | Angular Momentum | Required. Array of finite number; maximum items 256. |
| axis | Axis | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| projection | Projection | Required. Finite number. |
| magnitude | Magnitude | Required. Finite number. |
| signedShare | Normalized dot-product cosine; zero placeholder if defined=false. | Required. Finite number. |
| defined | Whether the associated ratio is defined; inspect before using a zero placeholder. | Required. Boolean. |
{
"input": {
"angularMomentum": [
3,
4,
0
],
"axis": [
1,
0,
0
]
},
"output": {
"projection": 3,
"magnitude": 5,
"signedShare": 0.6,
"defined": true
}
}Limitations and assumptions
- SignedShare is the directional cosine and can be negative. Inspect defined for the zero-vector placeholder; this projects a supplied vector without calculating it from masses or motion.
- 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).
- Angular Momentum Reference Point Shift
Shift angular momentum to an origin displaced by the supplied vector using L_new=L_old-displacement cross momentum.