A stretchy flag on the Moon
Grab the glowing top-right corner. Pull it away from the pole to stretch the cloth, then let go. Nothing blows it around: only your hand, the cloth, and lunar gravity.
The cloth is deliberately soft. At its teaching limit it stops extending rather than tearing. Try pulling outward, then down or up. Touch works too. Keyboard: focus the corner, Space to grab or release, arrows to pull. Escape lets go.
What is being modeled?
A 2.4 × 1.4 m sheet is attached only along its left edge. Each reference triangle assigns mass to three moving vertices. Its material directions determine finite strain: squared length changes along warp and weft, and their dot product for shear. The cloth chapter defines the reference-area energy, including directional coupling, that supplies all membrane corrections. There are no diagonal shear springs. Gravity and the current state determine the motion; no falling path is prescribed.
The illustrative sheet coefficients are extension 35 N/m, coupling 3.5 N/m and shear 0.35 N/m. They have the same meanings as the chapter’s material coefficients, with much softer extension. Green strain makes the law independent of rigid rotation and reduces to engineering strain for small changes; it does not make the law physically validated at large extension. A separate chapter-defined inequality limits each triangle’s two thread stretches to 55%. It does not bound every diagonal direction or simulate real tearing.
Bending uses the signed angle between adjacent triangle normals, weighted by original edge lengths and triangle areas, with chosen discrete rigidity 0.2 N m. These corrections derive from the chapter’s hinge energy, not from uneven in-plane stretching. Fixed-geometry refinement no longer makes bending energy collapse. This discrete law has directional grid bias, including a stronger response for oblique cylindrical bends, and is not a complete isotropic shell model. Numerical damping at 0.35/s and finite XPBD iterations make settling usable, not energy-conserving or calibrated. There is no self-contact, tearing, pole/ground contact or validated collapse treatment. Folds may overlap.
Gravity is based on NASA’s Moon Fact Sheet. The chapter develops the finite-strain and hinge energy laws and their sources. The compliant solver follows XPBD. All material coefficients are deliberate teaching choices.