Design of Head-Pursuit Guidance Law Based on Backstepping Sliding Mode Control

In order to meet the needs of high-precision guidance for intercepting hypersonic targets, a novel head-pursuit guidance law considering the dynamic characteristics of a missile control system and the target mobility is presented via combining a fast power reaching law with backstepping sliding mode control in this paper. Initially, a three-dimensional head-pursuit system model of the missile and target is established. Subsequently, the system model is decomposed into a pitch plane system and lateral plane system, the control system dynamics are equivalent to second-order systems, and finite-time disturbance observers are introduced to estimate the target accelerations. On the basis of the previous work, the head-pursuit guidance laws of the vertical system and the lateral system which can stabilize the closed-loop system are designed separately and strict proofs of the methods are given. Finally, simulations are carried out to verify the effectiveness of this head-pursuit guidance law.

Low-temperature expansion of the Casimir–Polder free energy for an atom interacting with a conductive plane

The low-temperature expansion of the free energy of an atom/plane system is considered for a general symmetric form of the tensor conductivity of the plane. It is shown that the first correction is proportional to the second order of the temperature [Formula: see text] and comes from the TM mode. The agreement of the expansion and exact expressions for different models of conductivity is numerically demonstrated.