In this paper there are presented interesting problems from cinematic or dynamic elds, solved by the authors using the inverse methods. These methods are important for systems optimization and control applications in industrial and/or economics area. 1. Plan robot problem. Considering the cinematic of roto-translation plate,there are considered the trajectory equations (T), the base (B) and the described curve (R) reported to the axial system. The robot is determined by two (contact-connected) plates ? the xed base (B) and the known (T) trajectory (the robot ?execute/fallow? the T trajectory and determine the R curve). Same time,corresponding problems exists: (R, T) given and B to be calculated. As solution, the Cauchy problem can be solved for (B, T) or (R, T) cases. Another plan robot that can turn o the oral trajectories can be obtained composing of two cinematic periodical moves. 2. The problem of heavy rigid solid with a xed point located in elastic eld. In this case, the prime integrals are determined in linear form and are in uenced by the choosing of inertial moments, of heavy center?s coordinates and of the initial conditions. The study is made for the giro-tachometer, in this case we havethe fourth degree Lagrange polynomial.3. The problem of automatic control with absolute stabilization and optimal command.The purpose of the studies is the automatic pilot stabilization based on Popov and Lurie methods. The optimal control is implemented using Pontreaguine extreme principle for rockets and multiple engines (propellants) ships. 4. The problem of the optimal ship?s design pro les from hydro-aero-dynamics elds used on extreme resistance / bearing.The inverse analytical problem leads to RiemannHilbert planarity problem and the integral singular equations and dynamics and geometric parameters determination is made by externality procedure of nonlinear functional.