The paper "Continuous Finite-Time Stabilization of the Translational and Rotational Double Integrators" by Sanjay P. Bhat and Dennis S. Bernstein addresses the problem of finite-time stabilization for the double integrator system, both in its translational and rotational forms. The authors use Lyapunov theory to prove finite-time convergence for continuous time-invariant feedback laws. For the rotational double integrator, they modify the controllers to avoid the "unwinding" phenomenon, where the body rotates multiple times before coming to rest. The paper presents a class of continuous finite-time-stabilizing feedback laws for the translational double integrator and a modified class of bounded continuous finite-time controllers. For the rotational double integrator, they propose a periodic feedback law that avoids unwinding. The results are based on Lyapunov theory for finite-time differential equations and are illustrated with phase portraits and examples. The paper also discusses the challenges and limitations of discontinuous controllers and the benefits of continuous controllers in terms of robustness and disturbance rejection.The paper "Continuous Finite-Time Stabilization of the Translational and Rotational Double Integrators" by Sanjay P. Bhat and Dennis S. Bernstein addresses the problem of finite-time stabilization for the double integrator system, both in its translational and rotational forms. The authors use Lyapunov theory to prove finite-time convergence for continuous time-invariant feedback laws. For the rotational double integrator, they modify the controllers to avoid the "unwinding" phenomenon, where the body rotates multiple times before coming to rest. The paper presents a class of continuous finite-time-stabilizing feedback laws for the translational double integrator and a modified class of bounded continuous finite-time controllers. For the rotational double integrator, they propose a periodic feedback law that avoids unwinding. The results are based on Lyapunov theory for finite-time differential equations and are illustrated with phase portraits and examples. The paper also discusses the challenges and limitations of discontinuous controllers and the benefits of continuous controllers in terms of robustness and disturbance rejection.