Tumbling Satellite Capture: Angular Momentum in Space Robotics

Target Tumble Axis

Initial spin rate 60°/s

Robotic Capture

Grapple offset from target CM 2.0 m

Closing speed 1.0 m/s

Free tumbling — chaser on standby

Live Telemetry

Spin rate ω

60.0°/s

|L| angular momentum

— kg·m²/s

System mass (target + chaser)

66 kg + 40 kg

How it works

The target is a bus with two solar panels, so its three principal moments of inertia are all different (I_x ≪ I_y < I_z here). With no external torque, Euler's rigid-body equation applies:

I·dω/dt = -ω × (I·ω)      (body-frame form)
equivalently: L = I(t)·ω(t) is CONSTANT in the world frame

Spinning about the axis of smallest or largest inertia (X or Z) is stable. Spinning about the intermediate axis (Y) is not — any tiny perturbation grows, and the body periodically flips end-over-end. This is the intermediate-axis / tennis-racket / Dzhanibekov theorem, and it matters for real missions: an uncontrolled satellite or debris object tumbles unpredictably, which is exactly why a servicing robot must plan its capture around the target's current spin state rather than a static pose.

At the instant of capture the grab is modelled as a perfectly inelastic, impulsive rigid attachment. Total angular momentum about the new combined center of mass is conserved:

L_total = L_target,spin + m_chaser·(r_chaser − R_cm) × v_chaser
ω_after = I_combined⁻¹ · L_total

A longer grapple offset or a faster closing speed both increase the chaser's orbital angular momentum contribution, so they change how hard the combined stack spins right after capture — a real design driver for on-orbit servicing and active-debris-removal arms, which must budget reaction wheels or thrusters to detumble whatever the capture leaves behind.

Target satellite Robotic chaser ω (angular velocity)

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.