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Based on the total time derivative along the trajectory of the time, we study the unified symmetry of Vacco dynamical systems. The definition and the criterion of the unified symmetry for the system are given. Three kinds of conserved quantities, i.e. the Noether conserved quantity, the generalized Hojman conserved quantity and the Mei conserved quantity, are deduced from the unified symmetry. An example is presented to illustrate the results. [ABSTRACT FROM AUTHOR]

This paper studies Mei symmetry which leads to a generalized Hojman conserved quantity for variable mass systems with unilateral holonomic constraints. The differential equations of motion for the systems are established, the definition and criterion of the Mei symmetry for the systems are given. The necessary and sufficient condition under which the Mei symmetry is a Lie symmetry for the systems is obtained and a generalized Hojman conserved quantity deduced from the Mei symmetry is got. An example is given to illustrate the application of the results. [ABSTRACT FROM AUTHOR]

This paper studies the unified symmetry of a nonholonomic system of non-Chetaev type with unilateral constraints in event space under infinitesimal transformations of group. Firstly, it gives the differential equations of motion of the system. Secondly, it obtains the definition and the criterion of the unified symmetry for the system. Thirdly, a new conserved quantity, besides the Noether conserved quantity and the Hojman conserved quantity, is deduced from the unified symmetry of a nonholonomic system of non-Chetaev type with unilateral constraints. Finally, an example is given to illustrate the application of the results. [ABSTRACT FROM AUTHOR]

This paper studies the perturbation to symmetries and adiabatic invariant for nonholonomic controllable mechanical systems with non-Chetaev type constraints. It gives the exact invariants introduced by the Lie symmetries of the nonholonomic controllable mechanical system with non-Chetaev type constraints without perturbation. Based on the definition of high-order adiabatic invariants of mechanical system, the perturbation of Lie symmetries for nonholonomic controllable mechanical system with non-Chetaev type constraints with the action of small disturbances is investigated, and a new type of adiabatic invariant of system are obtained. In the end of this paper, an example is given to illustrate the application of the results. [ABSTRACT FROM AUTHOR]

Introduction Intraoperative technical complications are occasionally encountered while implanting INTERTAN™ nails for intertrochanteric fractures. Surgeons need to pay attention to the difficulties they may encounter during the implantation of an INTERTAN™ nail. Case presentation We report four cases with intraoperative difficulties during the implantation of INTERTAN™ nails among Han Chinese patients from mainland China. In Case 1, during the operation on a 75-year-old woman, an anatomical specificity of excessive femoral shaft curvation at the coronal and sagittal planes was observed; a relatively smooth implantation was achieved by adjusting the entry point. In Case 2, due to fat obstruction, an INTERTAN™ nail was implanted at an oblique angle in 64-year-old obese woman, which resulted in an iatrogenic fracture of the proximal femur. In Case 3, an iatrogenic fracture of the distal femur developed in an 83-year-old woman because of violent hammering and underestimating of bone fragility. In Case 4, an iatrogenic fracture occurred in a 40-year-old woman around the distal locking slot during the drilling process. Conclusions Preoperative evaluation should be considered as an important preparation for the implantation of an INTERTAN™ nail. Full-length anteroposterior and lateral radiographs of the injured femur are necessary to confirm the anatomical specificity. The vertical trajectory as well as sufficient reaming is important in reducing the possibility of iatrogenic fractures, particularly for obese patients. In older patients, violent hammering should be avoided and full reaming is recommended even if the canal seems to be wide enough. For cases where hard fracture reduction is predicted, the strategy of open reduction and fixation with a dynamic hip screw seems to be more rational and should be considered as an alternative method. [ABSTRACT FROM AUTHOR]