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Impulsive problems for mechanical systems subject to kinematic constraints are discussed in this paper. In addition to the applied impulses, there may exist suddenly changed constraints, or termed impulsive constraints. To describe the states of the system during the impulsive motion, three different phases, i.e., prior motion, virtual motion, and posterior motion, are defined which are subject to different sets of constraints, and thus have different degrees-of-freedom. A fundamental principle, i.e., the principle of velocity variation, for the constrained impulsive motion is enunciated as a foundation to derive the privileged impulse-momentum equations. It is shown that for a system with no applied impulse, a conservation law can be stated as the conservation of the virtual-privileged momenta. The proposed methodology provides a systematic scheme to deal with various types of impulsive constraints, which is illustrated in the paper by solving the constrained impulsive problems for the motion of a sleigh.

A new class of non‐holonomic constraints is proposed, namely, completely non‐holonomic, partially non‐ holonomic, and truly non‐holonomic. The classification is mainly based on the Frobenius condition and the existence of the integral surfaces of the constraints. The intrinsic properties of non‐holonomic constraints, such as the reachability property, vary with respect to different classes. In fact, some non‐holonomic constraints do not have the reachability property. The path‐planning problems for different classes of non‐holonomic constraints also become quite delicate. The paths from a point on one side of the critical surface to a point on the other side must pass through the singular points on the critical surface. The observation made in this paper gives a new outlook of non‐holonomic constraints, and may lead to a deeper understanding of the behaviour of systems with non‐holonomic constraints.

Lifetime measurements of levels near 2 MeV in 114 Cd give quantitative evidence for collective 3-phonon vibrational states. An analysis of the level scheme reveals a remarkable ambiguity with origins in the basic properties of quantum mechanical mixing.

It is shown that isotopic sequences of 21+ level energies, for elements from Zr to the actinides, are linear against the factor P = N p N n (N p +N n ) . This linearity is interpreted in terms of a simple two-level model. The P-factor also provides a linearization scheme for intruder 0+ energies in the Pb region.

Calculations of the variations of residual proton-neutron (p-n) interaction matrix elements for three different mass regions are presented within the frameworks of two approaches, the Nilsson and shell models, which differ substantially in the basis states and interactions used. The excellent agreement obtained with experiment in both approaches points to the simplicity of the underlying physics in terms of orbital overlap arguments.

Introduction Long-term weight change since young-adulthood is a better indicator of distribution of body fat mass. We investigated weight change from age 20 in relation to the risk of CVD mortality, including specific causes of CVD, using data of a large population-based cohort study in Japan. Methods In 1994, 41 364 eligible individuals aged 40–79 years responded to the questionnaire survey. Participants were categorised by weight change: loss ≥10 kg and 5−9.9 kg, ±4.9 kg, gain 5−9.9 kg and ≥10 kg. During the follow-up period of 13.3 years, 1756 deaths of CVD were identified and risk analysis was done by Cox proportional hazards model. Results For all CVD mortality in men were significantly increased for weight loss more than 10 kg with the HR 1.52. Weight gain didn9t predict increased risk in our study. In women, U-shaped association was found while the HRs were 1.64 and 1.35 for those with 10 kg weight loss and weight gain, respectively. The risks for coronary and stroke mortality were also increased for women who lost their weight with the HRs 2.03 and 1.49. The risk trends were similar in subgroup analysis of elderly, non-smokers and early death deletion. Conclusion Weight loss since early adulthood was a predictor of death from CVD. Weight gain more than 10 kg was associated with increased risk of CVD mortality among women.