All Questions
Tagged with classical-mechanics reference-frames
30
questions with no upvoted or accepted answers
3
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What frame of refernce to select in statistical mechanics?
Suppose we have a solid particle suspended inside a fluid such as an ideal gas, as shown in the following picture:
Our system is the solid particle and the environment is the gas (which acts as a ...
3
votes
1
answer
137
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These components of the angular velocity are given in what reference frame?
When we have a rigid body, the rigidity constraint allows us to write the trajectory $\mathbf{r}_i$ of the $i$-th particle as
$$\mathbf{r}_i(t) = R(t)\mathbf{b}_i + \mathbf{w}(t),$$
where we are ...
3
votes
0
answers
130
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Gauge formalism in rigid body mechanics
When doing calculations in rigid body mechanics, it is necessary to choose an origin to calculate torques and angular momenta. However, the underlying dynamics does not depend upon the choice of that ...
2
votes
1
answer
675
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Possible error in Marion and Thornton's Classical Dynamics of Particles and Systems
I was going over my notes on classical mechanics and just started to review rotation matrices which is the first topic the book starts with. On page 3
The rotation matrix associated with 1.2a and 1....
1
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0
answers
36
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How do 4-vectors change under an "accelerated" Lorentz transformation?
I assume that an observer moving with velocity $\mathbf{v} = v\mathbf{n} = \mathbf{v}(t)$ (with respect to another observer) has coordinates
where $x^{\mu}$ are the coordinates for the observer who ...
1
vote
1
answer
92
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How to define differentiation of a time-dependent vectors with respect to a specific reference frame in a coordinate-free manner?
It is usual in classical mechanics to introduce the derivative of a time-dependent vector with respect to a reference frame. This is accomplished through the use of a basis that is fixed with respect ...
1
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0
answers
61
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Why does my toothbrush topple on rebound?
I noticed this with my toothbrush the other day, but I feel that I have witnessed it happening before.
I accidentally knocked my hand into my toothbrush (electric toothbrush, can stand upright on its ...
1
vote
0
answers
136
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Assumptions in Galilean and Relativistic Frame Transformation
While deriving the frame transformation equations, either the Galilean Transformation or Lorentz transformation. I have seen almost all authors mentioning/assuming that if an inertial frame $\textbf{S}...
1
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1
answer
83
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Doubt on the difference between a rotational coordinate system and spherical coordinate system and the calculation of the Christoffel sysmbols
I know basic differential geometry for general Relativity and classical mechanics. But an interesting fact was revealed in my calculations, namely, that I discovered that I didn't realize the ...
1
vote
0
answers
90
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Reference Frame conceptual confusion
I am getting confused as to why a ball still feels gravity when inside a moving car. The point of a reference frame is to reinterpret all the forces acting on a particle in one frame only. Hence all ...
1
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0
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403
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Angular velocities in moving reference frames
Please refer the image below for a clear idea of my question.
So, the instructor has written the angular velocity of the wheel, w.r.t. ground and the unit vectors he used are the ones for the frame B....
1
vote
0
answers
306
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Rigid Rotor, Heisenberg Picture
I'm running into a problem where a rigid rotor in the the (non-inertial) principle axis frame of reference seems to violate Ehrenfest's theorem by a minus sign.
Consider a rigid rotor with ...
0
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0
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65
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Justifying that the gold nucleus is at rest in a Rutherford experiment
This is an example on the Rutherford Experiment from Young and Freedman's University Physics.
In the last paragraph of the solution the book states that it is valid to assume that the gold nucleus ...
0
votes
0
answers
19
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2d elastic scattering with an impact parameter
Hello guys I have homework that has tasked me with connecting the effect of the scattering parameter to the energy transfer in a 2d elastic collision of two arbitrary spheres with one of them standing ...
0
votes
0
answers
14
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Reading on weighing scales at the equator of a moon in a tidally locked two-body system
I'm trying a made-up extension of this problem. Consider the planet Mars and its moon Deimos, which can be approximated as meeting the following simplifying conditions:
Both objects are perfect ...
0
votes
1
answer
44
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In terms of which zero should i calculate the potential energy in the Lagrangian formalism?
What I understand is that we have two kinds of coordinates when working with the Lagrangian formalism with different zeros (which may happen to coincide) to measure from, those are the Cartesian ...
0
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2
answers
61
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Inertial accelerations like the Coriolis effect are well known. Are there also 'inertial jerks' and what are some examples?
Inertial accelerations like the Coriolis effect are well known. Are there also 'inertial jerks' and what are some examples?
My guess would be that it would look something like:
$$ j=-3v_r \omega^2 e_r ...
0
votes
2
answers
176
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Lagrangian of inverted physical pendulum with oscillating base
An inverted physical pendulum is deviated by a small angle $\varphi$ and connected to an oscillating base with oscillation function $a(t)$. The pendulum's mass is $m$ and its center of mass is $l$ ...
0
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1
answer
126
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Using reduced mass to solve problems
A small block of mass $m$ rests on the bottom of a big box also of mass $m$. If the small block is then given a velocity $V$ to the right, how far has the box moved once the block has come to rest ...
0
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2
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521
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Decomposing Lagrangian into CM and relative parts with presence of uniform gravitational field
Most problems concerning two-body motion (using Lagrangian methods) often only consider the motion of two particles subject to no external forces. However, the Lagrangian should be decomposable into ...
0
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1
answer
115
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Transport theorem in spacecraft control: tracking a reference angular velocity
I am reading the book named "Analytical mechanics aerospaces systems" by Schaub and Junkins.
In section 7.2, the task is to control the spacecraft to track a specified angular velocity $w_r$ ...
0
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0
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76
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What is the English phrase for " loi de composition des accélérations" in French. ( Trans. " composition of accelerations law")
I'm looking for details regarding the derivation of a formula called in French" loi de composition des accélérations" ( " composition of accelerations law").
This law allows you ( ...
0
votes
1
answer
35
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Shaped objects positioned in a reference frame
If I have a shaped object (not a point) in a fixed 3-dim reference frame, I believe it takes 6 "pieces of information" to position it: $X, Y, Z$, and three orientation angles. If I add ...
0
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2
answers
156
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Generalized coordinates as components
Why we cannot express Generalized coordinates as a vector like we do with Cartesian coordinates $x$ , $y$ ,$z$ ?
0
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1
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307
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Derivative of angular velocity in a rotating frame
Taylor Relies on these relations
$v = \omega \times r$
$\frac{d}{dt}Q = \omega \times Q$
To show that
$a = a' + 2 \omega \times v' + \omega \times \omega \times r' + \alpha \times r' ...
0
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0
answers
108
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Establishing an inertial frame of reference by observing a closed mechanical system?
Suppose one has a closed system of $N$ material points with known masses, $m_1 ,..., m_N$ . Also given are their coordinates as functions of time, ${\bf r}_1(t), ..., {\bf r}_N(t)$, in some laboratory ...
0
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0
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113
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Lagrangian of free particle in non-inertial frame
As in Landau & Lifshitz 1st chapter
"If an inertial frame К is moving with an infinitesimal velocity e relative to another inertial frame K', then v' = v+e. Since the equations of motion must ...
0
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0
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404
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Re: Susskind and Hrabovsky: Should the Lagrangian of a particle referred to a rotating frame omit the velocity dependent "potential"?
My question pertains to Lecture 6: Exercise 4 in The Theoretical Minimum by Leonard Susskind and George Hrabovsky. A suggested solution has been posted here: http://www.madscitech.org/tm/slns/
The ...
0
votes
1
answer
53
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"Reference dependence of fuel gauges" in classical mechanics
The power exercised by a force on an object is dependent on the velocity of the object and hence the frame of reference. I am wondering wherein the error lies with arguments such as the ones presented ...
-1
votes
1
answer
34
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Kinetic energy problem for only one existing object
If only a single object were to exist in the universe, what would be the measure of its kinetic energy?I mean what would determine the velocity of the object?I could be one,or could be hunder thousand ...