Theoretical Mechanics Chapter 16: Theorem of virtual displacements
Theoretical Mechanics
理论力学 第十原
Dynamic In the first part, statics, we started from the axioms of statics, then obtained the equilibrium conditions of a rigid body by simplification of the system of forces. They are used to investigate equilibrium problems of rigid bodies and of system of rigid bodies. In this chapter, we shall introduce a theorem which is suitable to study equilibrium problems of any system of particle in general. Using the concepts of displacements and work, the theorem defines the equilibrium conditions for any system of particles. It is called the theorem of virtual displacements. It is the most general theorem to study equilibrium problems. In addition, combining it with D'Alembert's principle, we can obtain a general equation of dynamics which can be used to solve the problems of dynamics
3 In the first part, statics, we started from the axioms of statics, then obtained the equilibrium conditions of a rigid body by simplification of the system of forces. They are used to investigate equilibrium problems of rigid bodies and of system of rigid bodies. In this chapter, we shall introduce a theorem which is suitable to study equilibrium problems of any system of particles, in general. Using the concepts of displacements and work, the theorem defines the equilibrium conditions for any system of particles. It is called the theorem of virtual displacements. It is the most general theorem to study equilibrium problems. In addition, combining it with D‘Alembert’s principle, we can obtain a general equation of dynamics which can be used to solve the problems of dynamics
力单 在第一篇静力学中,我们从静力学公理出发,通过力系 的简化,得出刚体的平衡条件,用来研究刚体及刚体系统的 平衡问题。在这一章里,我们将介绍普遍适用于研究任意质 点系的平衡问题的一个原理,它从位移和功的概念出发,得 出任意质点系的平衡条件。该原理叫做虚位移原理。它是研 究平衡问题的最一般的原理,不仅如此,将它与达朗伯原理 相结合,就可得到一个解答动力学问题的动力学普遍方程
4 在第一篇静力学中，我们从静力学公理出发，通过力系 的简化，得出刚体的平衡条件，用来研究刚体及刚体系统的 平衡问题。在这一章里，我们将介绍普遍适用于研究任意质 点系的平衡问题的一个原理，它从位移和功的概念出发，得 出任意质点系的平衡条件。该原理叫做虚位移原理。它是研 究平衡问题的最一般的原理，不仅如此，将它与达朗伯原理 相结合，就可得到一个解答动力学问题的动力学普遍方程
Chapter 16: Theorem of virtual displacements □§16-1 Constraints and their classification D$16-2 Degrees of freedom and generalized coordinates D 816-3 Virtual displacements and virtual work 心§164 Ideal constraints D 8 16-5 Theorem of virtual displacements
5 §16–1 Constraints and their classification §16–2 Degrees of freedom and generalized coordinates §16–3 Virtual displacements and virtual work §16–4 Ideal constraints §16–5 Theorem of virtual displacements Chapter 16: Theorem of virtual displacements