Numerical record 001 · Phase-plane projection
θ–angular velocity phase-plane projection
A full-resolution rendering of a two-dimensional projection of the simulated angular trajectory, encoded at 60 frames per second with 4:4:4 chroma to preserve fine plotted lines.
- Field
- 50 Hz
- Window
- 3.0 s
- Range
- 20–175 s
- Video
- 1080² · 4:4:4
θ versus dθ/dt
Phase-plane evolution
Interpretation and limitations
Two-dimensional phase-plane projection
The plot places angular position θ on one axis and its time derivative dθ/dt on the other. Each point is sampled from the numerical trajectory. The plotted pair is a projection of the model’s full dynamical state, not a complete state description.
A 3 s window advances through the 20–175 s simulation interval. Nested or crossing curves indicate revisitation of similar values in this projection; a crossing does not establish equality of the omitted coordinates. The finite-time record is descriptive and does not establish periodicity or dynamical stability.
Serialized simulator inputs
Simulation parameters
Every value below is transcribed from the attached MBS parameter-set JSON. Original keys are retained for unambiguous reuse. Displayed digits reflect file serialization and do not represent independently established physical precision or measurement uncertainty.
| Parameter | JSON key | Value | Unit |
|---|---|---|---|
| Parameter-set name | name | half_height=1.74 gamma=5. mfg=2 xi=0.1 psidd=7.525 modified | — |
| Field frequency | field_frequency_hz | 50 | Hz |
| Principal inertia I₁ | inertia_1 | 1.0023 × 10−7 | kg·m2 |
| Principal inertia I₂ | inertia_2 | 1.0029061860928428 × 10−7 | kg·m2 |
| Principal inertia I₃ | inertia_3 | 1.4993938139071574 × 10−7 | kg·m2 |
| Product of inertia I₁₂ | inertia_12 | 0 | kg·m2 |
| Product of inertia I₁₃ | inertia_13 | 0 | kg·m2 |
| Product of inertia I₂₃ | inertia_23 | −1.7358898491225579 × 10−9 | kg·m2 |
| Magnetic coupling mB | magnetic_coupling | 0.0017 | J |
| Field tilt γ | field_tilt_deg | 5.6 | ° |
| Damping ξ | damping | 0.1 | s−1 |
| Spin acceleration | spin_acceleration | 7.438 | rad·s−2 |
| Initial θ | theta_deg | 42.43999818350852 | ° |
| Initial φ | phi_deg | 166.88460891423827 | ° |
| Initial ψ | psi_deg | 106.67243516221909 | ° |
| Initial θ rate | theta_rate | −16.18666248681155 | rad·s−1 |
| Initial φ rate | phi_rate | 292.35678474551474 | rad·s−1 |
| Initial ψ rate | psi_rate | −112.17252126319383 | rad·s−1 |
| Simulation duration | duration | 150 | s |
| Solver method | solver_method | LSODA | — |
| Relative tolerance | relative_tolerance | 1 × 10−12 | dimensionless |
| Absolute tolerance | absolute_tolerance | 1 × 10−13 | state-variable units* |
| Maximum solver step | maximum_step | 0.0002 | s |
| Steps per second | steps_per_second | 10,000 | steps·s−1 |
* Absolute tolerance is applied in each state variable’s own units; the numerical state combines dimensionless orientation components with angular-rate components.
Video encoding record
Video export metadata
Stream properties were checked against the MP4. Other values are transcribed from the attached export metadata and describe the visualization, not the solver’s physical validity.
Supplementary visualization · Limited documentation