Use of Synthetic Modes in Hybrid Coordinate Dynamic Analysis

The purpose of this paper is the introduction of the concept of "synthetic modes" and the development of the mathematical framework in which they may be used in the dynamic analysis of mechanical systems that can be idealized as a combination of rigid bodies and flexible appendages. (A typical mechanical system is a spacecraft composed of a semirigid primary structure to which very flexible deployed antennas or solar panels are attached.) For reasons noted in the paper, it may be desirable in the construction of equations of motion of such mechanical systems to employ a "hybrid" coordinate system, i.e., to employ position and attitude coordinates for the rigid bodies of the system and modal deformation coordinates for the elastic appendages. Synthetic modes are introduced in the process of truncating the modal coordinates without destroying the simulation of nonvibratory response of the flexible appendages. Although this can be accomplished also without the use of synthetic modes, the result is a heavily encumbered inertia matrix, which is explicitly time dependent for a vehicle of varying nominal configuration (e.g., a spacecraft with scanning antenna). With the use of as many as six synthetic modes each properly defined in terms of six "dead load coefficients," the equations of motion for the composite system may be constructed with a constant diagonal inertia matrix, even if the vehicle nominal geometry and attitude are slowly changing with time. The resulting efficiency in numerical integration provides the incentive for utilizing the synthetic modes.