On the requirements of interpolating polynomials for path motion constraints

In the framework of multibody dynamics, the path motion constraint enforces that a body follows a predefined curve being its rotations with respect to the curve moving frame also prescribed. The kinematic constraint formulation requires the evaluation of the fourth derivative of the curve with respect to its arc length. Regardless of the fact that higher order polynomials lead to unwanted curve oscillations, at least a fifth order polynomials is required to formulate this constraint. From the point of view of geometric control lower order polynomials are preferred. This work shows that for multibody dynamic formulations with dependent coordinates the use of cubic polynomials is possible, being the dynamic response similar to that obtained with higher order polynomials. The stabilization of the equations of motion, always required to control the constraint violations during long analysis periods due to the inherent numerical errors of the integration process, is enough to correct the error introduced by using a lower order polynomial interpolation and thus forfeiting the analytical requirement for higher order polynomials.

Mammography equipment

Mammography is one of the most technically demanding examinations in radiology, and it requires X-ray technology designed specifi cally for the task. The pathology to be imaged ranges from small (20–100 μm) high density microcalcifications to ill-defi ned low contrast masses. These must be imaged against a background of mixed densities. This makes demonstrating pathology challenging. Because of its use in asymptomatic screening, mammography must also employ as low a radiation dose as possible.