The Chern-Simons theory defined on a 3-dimensional manifold with boundary is written as a two-dimensional field theory defined only on the boundary of the three-manifold. The resulting theory is, essentially, the pullback to the boundary of a symplectic structure defined on the space of auxiliary fields in terms of which the connection one-form of the Chern-Simons theory is expressed when solving the condition of vanishing curvature. The counting of the physical degrees of freedom living in the boundary associated to the model is performed using Dirac's canonical analysis for the particular case of the gauge group SU (2). The result is that the specific model has one physical local degree of freedom. Moreover, the role of the boundary conditions on the original Chern-Simons theory is displayed and clarified in an example, which shows how the gauge content as well as the structure of the constraints of the induced boundary theory is affected.the curvature of the Lorentz connection ω I J . The variation of the action (18) with respect to the independent fields gives the equations of motion de I + ω I J ∧ e J = 0 and R IJ [ω] = 0 provided that ∂M 3 ε IJK e I ∧ δω JK vanishes. When we solve de I + ω I J ∧ e J = 0 for the connection ω I J in terms of the triad, namely, ω I J [e] and plug it back into the action (18), we recover, essentially, the Einstein-Hilbert action S[e] expressed in terms of the triads. There is no need of adding to S[e] the specific boundary conditions on the fields of the original action principle (18) that led to the original equations of motion.Let us come back to the Chern-Simons theory. One might be interested in keeping the original boundary conditions on the connection that kill (17) in the resulting field

Time boundary terms usually added to action principles are systematically handled in the framework of Dirac's canonical analysis. The procedure begins with the introduction of the boundary term into the integral Hamiltonian action and then the resulting action is interpreted as a Lagrangian one to which Dirac's method is applied. Once the general theory is developed, the current procedure is implemented and illustrated in various examples which are originally endowed with different types of constraints.

Time boundary terms usually added to action principles are systematically handled in the framework of Dirac's canonical analysis. The procedure begins with the introduction of the boundary term into the integral Hamiltonian action and then the resulting action is interpreted as a Lagrangian one to which Dirac's method is applied. Once the general theory is developed, the current procedure is implemented and illustrated in various examples which are originally endowed with different types of constraints.

Compliant mechanisms perform precision movements generated by the elastic deformation of their flexible elements. For most applications, resonance frequencies must be bounded by a defined range of values. Therefore, a modal analysis of the mechanisms is required at the initial stage of design. In this work, a novel flexible platform with 2 degrees of rotational freedom restricted by beam-type flexure elements is analyzed. The Screw Theory description of the movement of the mechanism is used for the rigid and the flexible elements. Using this formalism, the stiffness and mass matrices for a two-node beam element are derived and can be assembled using a standard finite-element-like procedure to perform the modal analysis of the mechanism. Starting from the desired movements, the mechanism is synthesized using screws and a hybrid (series/parallel) solution is proposed. The analytical results for the modal analysis obtained by Screw Theory are compared with the results of finite element analysis. Due to the computational efficiency, the analytical equations are chosen to be applied in the optimization of the designs.