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pallab
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what is the difference between δ- variation and ∆-variation in variational principle, used in classical mechanics?
Typically, ##\Delta## is not a variation but an ##\textit{actual}## difference, e.g. ##\Delta f= f(x_2)-f(x_1)##.pallab said:what is the difference between δ- variation and ∆-variation in variational principle, used in classical mechanics?
pallab said:what is the difference between δ- variation and ∆-variation
Which is why it is important to give the sourc(es) of where you saw δ-variation and ∆-variation. You can't depend on all textbooks and web sites using the same standard definition.muscaria said:Typically,
Can't speak for anyone else, but I reserve [tex]\Delta[/tex] for changes in the uncertainty, say between time and energypallab said:what is the difference between δ- variation and ∆-variation in variational principle, used in classical mechanics?
δ- VARIATION :-pallab said:what is the difference between δ- variation and ∆-variation in variational principle, used in classical mechanics?
You are replying to a thread which is more than 5 years old.Kulkarni Sourabh said:δ- VARIATION :-
In δ- variation process, we are compared all imaginary paths connecting two given points A & B at to given times t1 & t2 . The system must be travel from one end A to another end point B in the same time. The system point is separated up or slow down in order to make the total travel time along the path.
∆- VARIATION :-
In ∆- variation the process we shall restrict the comparison to all paths involving conservation of energy. Thus , in ∆- variation , the system point is separated up or slow down in order to make Hamiltonian constant along actual & varied path.
Reference: https://www.physicsforums.com/threads/difference-between-d-and-variation.923212/
The symbols δ and ∆ are used to represent different types of variation in scientific contexts. δ typically represents a small, incremental change, while ∆ represents a larger, overall change.
In mathematics, δ (delta) is often used to represent a small change or difference in a variable, while ∆ (delta) is used to represent a finite change or difference in a variable.
In physics, δ (delta) is used to represent a small change in a physical quantity, while ∆ (delta) is used to represent a finite change. These symbols are commonly used in equations and formulas to denote infinitesimal and finite changes, respectively.
In chemistry, δ (delta) is often used to represent a small difference or deviation in a measured quantity, while ∆ (delta) is used to represent a more significant change or difference. These symbols are commonly used in chemical equations to show changes in reactants and products.
No, δ and ∆ should not be used interchangeably. While they may both represent variation or change in a quantity, they have different connotations and specific uses in different scientific fields. It is important to use the correct symbol for the specific type of variation being described.