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Results tagged with classical-mechanics
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user 164464
Classical mechanics discusses the behaviour of macroscopic bodies under the influence of forces (without necessarily specifying the origin of these forces). If it's possible, USE MORE SPECIFIC TAGS like [newtonian-mechanics], [lagrangian-formalism], and [hamiltonian-formalism].
3
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Non-Holonomic constraints
I am struggling to understand how to determine whether the constraints are nonholonomic.
For an example:
"Consider a disk which rolls without slipping across the horizontal plane, what is the best ge …
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3
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0
answers
88
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Help with Newton's 3rd law
I am using the book Classical Dynamics of Particles and Systems by STEPHEN T. THORNTON, JERRY B. MARION and they say that Newton's 3rd law only applies when forces are $\textbf{central forces}$, basic …
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2
answers
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Perturbation Method: What is the acceptable method to terminate expansion
I am using the book Classical Dynamics of Particles and Systems by STEPHEN T. THORNTON, JERRY B. MARION, page: 67 and they use perturbation method to approximate:
\begin{equation} T = \frac{kV + g}{g …
- 283
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Using normal displacement instead of virtual displacement
I know that there are many posts about virtual displacement, but I want to answer the question if of: is virtual displacement is always needed to get the same results? I am going through a PDF by Subh …
- 283
0
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2
answers
81
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Help with deriving the Euler-Lagrange equation (evaluating at $ \varepsilon = 0$ before solv...
I am using wiki here to help me understand the deriving of the euler-lagrage equations
How do we get from:
\begin{equation}
\left.\frac{dJ_\varepsilon}{d\varepsilon}\right|_{\varepsilon = 0} = \int_a^ …
- 283
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0
answers
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Help with deriving euler-lagrange equation (evaluating at $ \varepsilon = 0$ before solving ... [duplicate]
I am using wiki here to help me understand the deriving of the euler-lagrage equations
How do we get from:
\begin{equation}
\left.\frac{dJ_\varepsilon}{d\varepsilon}\right|_{\varepsilon = 0} = \int_a^ …
- 283
0
votes
1
answer
87
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Help with understanding virtual displacement in Lagrangian
I know that these screen shots are not nice but I have a simple question buried in a lot of information
My question
Why can't we just repeat what they did with equation (7.132) to equation (7.140) wit …
- 283
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Accepted
Help with understanding virtual displacement in Lagrangian
Before answering the 2 questions I would like to provide some background.
Notes
As the Lagrangian is the function $L(x_i,\dot{x}_i)$, which is the function of 2 variables $x_i,\dot{x}_i$. Thus the par …
- 283
0
votes
1
answer
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Generalized forces for virtual work - Why did they drop the summation?
I am going through a PDF by Subhankar Ray & J. Shamanna on virtual work here and according to the PDF, equation 29, they write gerneralized force as:
$$Q_j = -\nabla_k\tilde{V}\cdot\left(\frac{\part …
- 283
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Non-integrable differential equation and non-holonomic contraints
In classical mechanics, holonomic constraints are relations between the position variables (and possibly time) that can be expressed in the following form: $g(y,t) = 0$
Nonholonomic constraints is whe …
- 283
0
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answer
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For virtual displacement in the Lagrangian, why is $\delta \dot{x_i} = \delta \frac{dx_i}{dt...
I am having trouble understanding why $$\delta \dot{x_i} = \delta \frac{dx_i}{dt} = \frac{d}{dt}\delta x_i \equiv 0.\tag{7.132}$$
you can see my explanation leading up to it below.
I would greatly app …
- 283
0
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0
answers
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Question on non-holonomic constraints (This is different to the others)
I know there are many posts on non-holonomic constraints and also many on this exact one but I feel that there is still some confusion on it.
"Consider a disk which rolls without slipping across the …
- 283