Virtual displacement and differential are both mathematical concepts used in mechanics to describe small changes in a system. However, they have different definitions and applications.
Virtual displacement is a hypothetical displacement that is assumed to occur in a system without actually physically moving any of its components. It is used in the principle of virtual work to analyze the equilibrium of a system.
Virtual displacement is used to determine the equilibrium of a system by considering the forces and moments acting on it. It allows for a simplified analysis of complex systems and is often used in structural engineering and mechanics.
Differential is a small change in a variable or function with respect to another variable. It is used in calculus to calculate rates of change and find maximum or minimum values of functions.
Differential has many practical applications in various fields such as physics, engineering, economics, and biology. It is used to model and analyze real-world phenomena, make predictions, and optimize systems.