- #1
blueberrypies
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[tex]\underbrace{d}_{dt}[/tex] ([tex]\dot{x}[/tex])[tex]^{2}[/tex] = 2[tex]\ddot{x}[/tex] ? or is it just 2[tex]\dot{x}[/tex] ?
Understanding the Derivative of Angular Velocity in Lagrangian Mechanics
- Thread starter blueberrypies
- Start date
In summary, the conversation is about a mathematical equation involving the chain rule and a symbol θ'. The participants are discussing whether the equation should be ∂L/∂t or ∂L/∂θ' and it is clarified that the latter is correct.
- #2
tiny-tim
Science Advisor
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welcome to pf!
hi blueberrypies! welcome to pf!
neither
…
use the chain rule
hi blueberrypies! welcome to pf!
neither
…use the chain rule
- #3
blueberrypies
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nevermind. I'm going to work on this more.
- #4
- #5
tiny-tim
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no, that would be ∂L/∂t
for ∂L/∂θ', remember that θ' is just a symbol, you can replace it by x (or anything), and forget the '
for ∂L/∂θ', remember that θ' is just a symbol, you can replace it by x (or anything), and forget the '
- #6
blueberrypies
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- 0
tiny-tim said:no, that would be ∂L/∂t
for ∂L/∂θ', remember that θ' is just a symbol, you can replace it by x (or anything), and forget the '
Ohhh!
I see what you are saying :) Thanks!
FAQ: Understanding the Derivative of Angular Velocity in Lagrangian Mechanics
What are the steps to check if an equation is correct?
To check if an equation is correct, you should follow these steps:
- Step 1: Simplify both sides of the equation by combining like terms.
- Step 2: Isolate the variable on one side of the equation by using inverse operations.
- Step 3: Check your solution by plugging it back into the original equation.
- Step 4: If the solution satisfies the equation, then the equation is correct.
How can I tell if my equation is balanced?
An equation is balanced if both sides of the equation have equal values. In other words, the equation is balanced when both sides have the same number of variables and the same coefficients.
Can an equation be true for some values but not others?
Yes, an equation can be true for some values but not others. This is known as a conditional equation. The values that make the equation true are called the solution set.
What is the purpose of balancing an equation?
The purpose of balancing an equation is to ensure that the equation is mathematically correct. Balancing an equation ensures that the values on both sides of the equation are equal and helps to find the solution to the equation.
Is there a specific order in which I should solve an equation?
Yes, there is a specific order in which you should solve an equation. This order is known as the Order of Operations, which states that you should solve equations using the following order: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).