Lagrange–d'Alembert principle

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In summary, the Lagrange–d'Alembert principle, also known as the virtual work principle, is a fundamental principle in classical mechanics that states that the motion of a system is determined by the difference between the potential and kinetic energy of the system. It was developed by mathematician Joseph-Louis Lagrange and physicist Jean le Rond d'Alembert in the 18th century, and is used in physics to find the equations of motion for a system by minimizing the action of the system. This principle differs from Newton's second law in that it takes into account both forces and energy to determine motion. Some practical applications of the Lagrange–d'Alembert principle include analyzing complex systems in fields such as mechanics,
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MPavsic
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Second and Third Newton Law
Hi, I am brainstorming about Dark Energy.

Lagrange–d'Alembert principle is stating that sum of external forces on the system of rigid bodies and sum of system forces must be in quasi static equilibrium.

What if there are no external forces acting on system of bodies and vector summation, relative to fixed reference frame of all m*a in the system of bodies is not equal to zero; would d'Alembert principle still hold?
 
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I have to add; Fixed reference frame is attached to the center of the Galaxy.
 

What is the Lagrange-d'Alembert principle?

The Lagrange-d'Alembert principle, also known as the virtual work principle, is a fundamental concept in classical mechanics that states that the equations of motion for a system can be derived from the principle of least action.

Who developed the Lagrange-d'Alembert principle?

The Lagrange-d'Alembert principle was first developed by mathematician Joseph-Louis Lagrange and physicist Jean le Rond d'Alembert in the 18th century.

What is the significance of the Lagrange-d'Alembert principle?

The Lagrange-d'Alembert principle is significant because it provides a powerful and elegant method for solving problems in classical mechanics. It allows for the derivation of equations of motion without the need for complex and lengthy calculations.

How is the Lagrange-d'Alembert principle applied in practice?

The Lagrange-d'Alembert principle is applied in practice by using it to derive the equations of motion for a system, which can then be used to predict the future behavior of the system. It is commonly used in fields such as engineering, physics, and astronomy.

What are some examples of systems where the Lagrange-d'Alembert principle is applicable?

The Lagrange-d'Alembert principle can be applied to a wide range of systems, including simple mechanical systems like a pendulum or a spring-mass system, as well as more complex systems like a rotating rigid body or a system of coupled oscillators. It can also be used in non-mechanical systems, such as electrical circuits and fluid dynamics problems.

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