A new concept in mechanics is proposed based on the notions of space, time, and energy. The energy is represented by the sum of thirteen terms expressed as products of invariants of the Lagrangian equations of motion and scalar factors corresponding to the physical properties of materials. Differential equations of motion and equilibrium are derived from the frame indifference condition for energy, in which the Eulerian variables are the sought functions and the Lagrangian variables are the arguments. Assumptions are made under which these equations can be transformed into the Poisson and Laplace equations. The law of conservation of energy is used to obtain dependences between the Lagrangian stresses and strains in the reversible deformation region; they are compared with the expressions used in the theory of elasticity. It is discussed whether the point of reference for the mean stresses may be chosen with regard to the volume energy density of particles in their initial state, as well as whether elastic deformation can be described using a single constant. As an example, the energy model and the equations of motion in the Lagrangian form are applied to describe the transition from reversible to irreversible deformation. The developed model differs from the classical one by using two independent infinitesimal operators for the time and space. It is shown that Newton’s law of inertia can be regarded as a variant for the determination of the generalized forces characterizing the kinetic energy change in a body with increments in the distance between the origin of the observer coordinate system and the center of mass of the body. The application of the Lagrangian variables and the superposition principle for describing any spatial motions (including for absolutely rigid bodies), which can be used in the dynamic analysis of linkages and other mechanisms, is validated. The multiple choice of generalized forces for absolutely rigid bodies, including when passive forces arise, is considered. The method of dynamic analysis of mechanisms developed on the basis of the energy model allows the law of conservation of energy to be satisfied for any part of the studied system in an arbitrary time interval.

中文翻译：

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基于空间、时间和能量概念的力学新概念

基于空间、时间和能量的概念，提出了一个新的力学概念。能量由十三个项的总和表示，这些项表示为拉格朗日运动方程的不变量和对应于材料物理特性的标量因子的乘积。运动和平衡的微分方程是从能量的框架无差异条件导出的，其中欧拉变量是寻求函数，拉格朗日变量是参数。假设这些方程可以转化为泊松方程和拉普拉斯方程。利用能量守恒定律得到可逆变形区拉格朗日应力应变之间的相关性；它们与弹性理论中使用的表达式进行了比较。讨论了是否可以根据粒子在初始状态下的体积能量密度来选择平均应力的参考点，以及是否可以使用单个常数来描述弹性变形。例如，应用能量模型和拉格朗日形式的运动方程来描述从可逆变形到不可逆变形的转变。所开发的模型与经典模型不同，它在时间和空间上使用两个独立的无穷小算子。结果表明，牛顿惯性定律可以看作是确定表征物体动能变化的广义力的变体，随着观察者坐标系原点和物体质心之间的距离的增加. 拉格朗日变量和叠加原理在描述任何空间运动（包括绝对刚体）方面的应用，可用于连杆和其他机构的动态分析，得到了验证。考虑了绝对刚体的广义力的多种选择，包括当被动力出现时。在能量模型的基础上开发的机制动态分析方法允许在任意时间间隔内对所研究系统的任何部分都满足能量守恒定律。包括当被动力量出现时，被考虑。在能量模型的基础上开发的机制动态分析方法允许在任意时间间隔内对所研究系统的任何部分都满足能量守恒定律。包括当被动力量出现时，被考虑。在能量模型的基础上开发的机制动态分析方法允许在任意时间间隔内对所研究系统的任何部分都满足能量守恒定律。