Illustrative numerical model • Not flight validated

Take control
of the tumble.

Explore the model in motion. Set the target’s spin, engage the model controller, and compare still-magnet and spinning-field modes.

Uploaded model / Perspective view

01Standby
02Approach
03Detumble
04Threshold

Initializing model.

Simulated values only. Synthetic camera observations, schematic arm geometry and local-patch drag; the visible magnet angle does not drive the torque calculation. Spacecraft reaction, thermal effects and orbital motion are not modeled. Read the model limits ↓

01 / Set target spin

Roll · X2.3°/s

Pitch · Y33°/s

Yaw · Z2.9°/s

Illustrative angular rates about the target’s own axes. Applying a preset changes model spin; dragging the target adds a spin impulse.

02 / Compare model modes

The controller chooses a sweep direction using its estimated state. Arbitrary magnet rotation does not always brake.

03 / Playback speed

Model seconds are numerical simulation time, not a physical stopping-time forecast.

Completed model runs

Model threshold runs appear here. These are simulated durations, not stopping-time predictions.

Target-centered frameBody axesEstimated spin ω̂Momentum HModel placement / dissipation

Simulated telemetry

All readouts below are model states or estimates. None are measured spacecraft values.

Synthetic sensor

—

Model spin

Estimated spin

—

Model estimate error

—

Momentum remaining

100

Energy remaining

100

Model hull gap

parked

Sweep velocity proxy

Last 60 model seconds

Model methods & limitations

Inspect the numerical model

What this model computes

01 · MODEL THE TUMBLE

A rigid body with three different moments of inertia

The numerical model integrates rigid-body Euler equations for ω, with a quaternion attitude q. Angular velocity uses RK4 while torque is held fixed within each step. Quaternion updates are normalized. The body dimensions and inertias are illustrative model inputs, not measured spacecraft values.

$I \dot{ω} + ω \times (I ω) = τ \dot{q} = \frac{1}{2} q \otimes [0, ω]$
02 · FIND THE FIXED ARROW

Angular momentum doesn't wander

In the ideal torque-free equations, angular momentum H is fixed in an inertial frame. Here the planner scores candidate positions by the torque component opposing the estimated H. It does not compute the receiving spacecraft’s reaction dynamics.

$H = R (q) I ω \frac{d H}{d t} = τ$
03 · SEE IT

Synthetic attitude observations

At 15 samples per model second, the code takes the model’s true attitude and adds seeded noise to produce q̃. A filter predicts and corrects attitude and spin. The inset is a rendered camera view with synthetic feature markers; it does not run image-based feature detection or pose solving. Loss of model lock disables commanded sweep while arm positioning continues.

$δ θ = 2 vec ({\hat{q}}^{- 1} \otimes \tilde{q})$ $\hat{q} \leftarrow \hat{q} \otimes \exp (α δ θ), \hat{ω} \leftarrow \hat{ω} + \frac{β}{Δ t} δ θ$
04 · DECIDE WHERE, BY PREDICTION

Score a short model prediction

The planner samples 260 directions, excludes directions on the far side, and scores the rest against a 1.5-model-second torque-free attitude prediction. Reach and position-change weights affect the score, refreshed every 0.4 model seconds. The keep-out sphere uses the box dimensions; protrusions and the full arm are not collision checked. The arm is a geometric two-link rendering, not a constrained robot IK or actuator simulation.

$S (d) = - \hat{H} \cdot \sum_{k = 1}^{15} τ (d; {\hat{q}}_{k}, {\hat{ω}}_{k}) Δ t \times w (d)$
05 · BRAKE WITHOUT CONTACT

Phenomenological local-patch drag

The code chooses the closest clamped point on the box hull, applies a gap-dependent drag to relative tangential velocity, and takes its moment about the center of mass. This is a phenomenological local-patch model. It does not solve electromagnetic fields, current distributions, conductivity, skin depth, magnet dimensions or thermal response. The glow indicates a model quantity; it is not a solved eddy-current image.

$v_{rel} = ω \times r_{p} - v_{f} F = - k B {(g)}^{2} [v_{rel} - (v_{rel} \cdot \hat{e}) \hat{e}]$ $τ = r_{p} \times F B (g) = B_{0} {(\frac{a}{a + g})}^{3}$
06 · COMMAND A MODEL SWEEP

A commanded sweep and schematic magnet

In spinning mode, the controller commands a local field-velocity proxy opposite the estimated hull motion, limited by G = 2.5 and the model speed cap. The red/blue magnet is drawn as diametric poles rotating around its shaft. Its visible angle is schematic and does not enter the torque calculation. The expression below is conditional on this local drag approximation; arbitrary magnet rotation does not always brake a target.

$v_{f} = - s {\hat{u}}_{t}, s = \min (s_{\max}, G | v_{t} |)$ $\frac{d T}{d t} = F \cdot v_{t} = - k B^{2} {| v_{t} |}^{2} (1 + G \cos φ) < 0 when \cos φ > - \frac{1}{G}$

Model assumptions

All rates, lengths, energies, durations and thresholds shown here are simulated outputs from illustrative inputs. The export describes scaled braking strength. No real stopping time, efficacy or measured performance is established.
The spacecraft holds a fixed position. Spacecraft reaction, thermal effects and orbital motion are not modeled. Detumbling does not remove an object from orbit.
The estimator uses deliberately perturbed inertia inputs and true model attitude plus noise. This does not establish real camera accuracy or AI performance.
The threshold uses filtered estimated spin, not a verified physical capture criterion. Passive model drag remains while the controller is in standby or the commanded sweep is zero.
This browser model includes pause/replay, responsive view fitting and interactive orbit, zoom and target-spin controls.

Illustrative numerical model; no flight validation.

What this model computes

A rigid body with three different moments of inertia

Angular momentum doesn't wander

Synthetic attitude observations

Score a short model prediction

Phenomenological local-patch drag

A commanded sweep and schematic magnet