In comparison with existing approaches, which struggle with scalability, communication dependency, and robustness against dynamic failures, cooperative aerial transportation via robot swarms holds transformative potential for logistics and disaster response. Here, we present a physics-inspired cooperative transportation approach for flying robot swarms that imitates the dissipative mechanics of table-leg load distribution. By developing a decentralized dissipative force model, our approach enables autonomous formation stabilization and adaptive load allocation without the requirement of explicit communication. Based on local neighbor robots and the suspended payload, each robot dynamically adjusts its position. This is similar to energy-dissipating table leg reactions. The stability of the resultant control system is rigorously proved. Simulations demonstrate that the tracking errors of the proposed approach are 20%, 68%, 55.5%, and 21.9% of existing approaches under the cases of capability variation, cable uncertainty, limited vision, and payload variation, respectively. In real-world experiments with six flying robots, the cooperative aerial transportation system achieved a 94% success rate under single-robot failure, disconnection events, 25% payload variation, and 40% cable length uncertainty, demonstrating strong robustness under outdoor winds up to Beaufort scale 4. Overall, this physics-inspired approach bridges swarm intelligence and mechanical stability principles, offering a scalable framework for heterogeneous aerial systems to collectively handle complex transportation tasks in communication-constrained environments.