What is the difference between a translation and a Galilean transformation?time invariance for...
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What is the difference between a translation and a Galilean transformation?
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What is the difference between a translation and a Galilean transformation?
newtonian-mechanics inertial-frames definition galilean-relativity
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What is the difference between a translation and a Galilean transformation?
newtonian-mechanics inertial-frames definition galilean-relativity
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What is the difference between a translation and a Galilean transformation?
newtonian-mechanics inertial-frames definition galilean-relativity
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What is the difference between a translation and a Galilean transformation?
newtonian-mechanics inertial-frames definition galilean-relativity
newtonian-mechanics inertial-frames definition galilean-relativity
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4 Answers
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In a Galilean transformation:
$$
x’=x-V_x t,qquad y’=y-V_yt, ,qquad z’=z-V_z t, ,qquad t’=t
$$
whereas in (spatial) translation
$$
x’=x-r_x, ,qquad y’=y-r_y, ,qquad z’=z-r_z, ,qquad t’=t, .
$$
The Galilean transformation depends explicitly on the relative velocity $vec V$ and the time $t$: for different $t$’s you add a different vector $vec V t$, whereas the simple translation adds a fixed time-independent vector $vec r$ to each coordinate.
Since the bit you add in the Galilean transformation is time-dependent, it affects how velocities transform:
$$
vec v’=vec v-vec V
$$
whereas, for a simple translation, $vec v’=vec v$ since there is no time-dependence on the shift in position.
answered yesterday
ZeroTheHeroZeroTheHero
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A Galilean transformation is a translation per unit time: whereas a translation just displaces all space by some vector, a Galilean transformation displaces space by some vector that is different at different moments in time. More precisely, it depends linearly on time.
If you've encountered spacetime diagrams before: on an (x, t) spacetime diagram, a translation would just be shifting the whole of the diagram to the right or to the left, whereas a Galilean transformation involves skewing the diagram.
answered yesterday
MovpasdMovpasd
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A Galilean transformation (or “Galilean boost”) is a change to a second inertial reference frame that is moving with constant velocity relative to the first one, but where the origin and axes align, so there is no translation at $t=0$ and no rotation at any time.
Imagine a bicyclist passing by you. His frame is boosted from yours. Yours is boosted from his, in the opposite direction.
Galilean boosts are the Newtonian equivalent of Lorentz boosts in Special Relativity.
In a translation, the frames do not have any relative motion. They just have different origins (but aligned axes).
answered yesterday
G. SmithG. Smith
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A galilean boost changes your reference frame. A translation only changes your position in the same reference frame.
answered 22 hours ago
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4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
In a Galilean transformation:
$$
x’=x-V_x t,qquad y’=y-V_yt, ,qquad z’=z-V_z t, ,qquad t’=t
$$
whereas in (spatial) translation
$$
x’=x-r_x, ,qquad y’=y-r_y, ,qquad z’=z-r_z, ,qquad t’=t, .
$$
The Galilean transformation depends explicitly on the relative velocity $vec V$ and the time $t$: for different $t$’s you add a different vector $vec V t$, whereas the simple translation adds a fixed time-independent vector $vec r$ to each coordinate.
Since the bit you add in the Galilean transformation is time-dependent, it affects how velocities transform:
$$
vec v’=vec v-vec V
$$
whereas, for a simple translation, $vec v’=vec v$ since there is no time-dependence on the shift in position.
answered yesterday
ZeroTheHeroZeroTheHero
22.8k5 gold badges35 silver badges71 bronze badges
$endgroup$
add a comment |
$begingroup$
In a Galilean transformation:
$$
x’=x-V_x t,qquad y’=y-V_yt, ,qquad z’=z-V_z t, ,qquad t’=t
$$
whereas in (spatial) translation
$$
x’=x-r_x, ,qquad y’=y-r_y, ,qquad z’=z-r_z, ,qquad t’=t, .
$$
The Galilean transformation depends explicitly on the relative velocity $vec V$ and the time $t$: for different $t$’s you add a different vector $vec V t$, whereas the simple translation adds a fixed time-independent vector $vec r$ to each coordinate.
Since the bit you add in the Galilean transformation is time-dependent, it affects how velocities transform:
$$
vec v’=vec v-vec V
$$
whereas, for a simple translation, $vec v’=vec v$ since there is no time-dependence on the shift in position.
answered yesterday
ZeroTheHeroZeroTheHero
22.8k5 gold badges35 silver badges71 bronze badges
$endgroup$
add a comment |
$begingroup$
In a Galilean transformation:
$$
x’=x-V_x t,qquad y’=y-V_yt, ,qquad z’=z-V_z t, ,qquad t’=t
$$
whereas in (spatial) translation
$$
x’=x-r_x, ,qquad y’=y-r_y, ,qquad z’=z-r_z, ,qquad t’=t, .
$$
The Galilean transformation depends explicitly on the relative velocity $vec V$ and the time $t$: for different $t$’s you add a different vector $vec V t$, whereas the simple translation adds a fixed time-independent vector $vec r$ to each coordinate.
Since the bit you add in the Galilean transformation is time-dependent, it affects how velocities transform:
$$
vec v’=vec v-vec V
$$
whereas, for a simple translation, $vec v’=vec v$ since there is no time-dependence on the shift in position.
answered yesterday
ZeroTheHeroZeroTheHero
22.8k5 gold badges35 silver badges71 bronze badges
$endgroup$
In a Galilean transformation:
$$
x’=x-V_x t,qquad y’=y-V_yt, ,qquad z’=z-V_z t, ,qquad t’=t
$$
whereas in (spatial) translation
$$
x’=x-r_x, ,qquad y’=y-r_y, ,qquad z’=z-r_z, ,qquad t’=t, .
$$
The Galilean transformation depends explicitly on the relative velocity $vec V$ and the time $t$: for different $t$’s you add a different vector $vec V t$, whereas the simple translation adds a fixed time-independent vector $vec r$ to each coordinate.
Since the bit you add in the Galilean transformation is time-dependent, it affects how velocities transform:
$$
vec v’=vec v-vec V
$$
whereas, for a simple translation, $vec v’=vec v$ since there is no time-dependence on the shift in position.
answered yesterday
ZeroTheHeroZeroTheHero
22.8k5 gold badges35 silver badges71 bronze badges
edited 21 hours ago
answered yesterday
ZeroTheHeroZeroTheHero
22.8k5 gold badges35 silver badges71 bronze badges
answered yesterday
ZeroTheHeroZeroTheHero
22.8k5 gold badges35 silver badges71 bronze badges
answered yesterday
ZeroTheHeroZeroTheHero
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22.8k5 gold badges35 silver badges71 bronze badges
add a comment |
add a comment |
$begingroup$
A Galilean transformation is a translation per unit time: whereas a translation just displaces all space by some vector, a Galilean transformation displaces space by some vector that is different at different moments in time. More precisely, it depends linearly on time.
If you've encountered spacetime diagrams before: on an (x, t) spacetime diagram, a translation would just be shifting the whole of the diagram to the right or to the left, whereas a Galilean transformation involves skewing the diagram.
answered yesterday
MovpasdMovpasd
513 bronze badges
New contributor
Movpasd is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
A Galilean transformation is a translation per unit time: whereas a translation just displaces all space by some vector, a Galilean transformation displaces space by some vector that is different at different moments in time. More precisely, it depends linearly on time.
If you've encountered spacetime diagrams before: on an (x, t) spacetime diagram, a translation would just be shifting the whole of the diagram to the right or to the left, whereas a Galilean transformation involves skewing the diagram.
answered yesterday
MovpasdMovpasd
513 bronze badges
New contributor
Movpasd is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
A Galilean transformation is a translation per unit time: whereas a translation just displaces all space by some vector, a Galilean transformation displaces space by some vector that is different at different moments in time. More precisely, it depends linearly on time.
If you've encountered spacetime diagrams before: on an (x, t) spacetime diagram, a translation would just be shifting the whole of the diagram to the right or to the left, whereas a Galilean transformation involves skewing the diagram.
answered yesterday
MovpasdMovpasd
513 bronze badges
New contributor
Movpasd is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
A Galilean transformation is a translation per unit time: whereas a translation just displaces all space by some vector, a Galilean transformation displaces space by some vector that is different at different moments in time. More precisely, it depends linearly on time.
If you've encountered spacetime diagrams before: on an (x, t) spacetime diagram, a translation would just be shifting the whole of the diagram to the right or to the left, whereas a Galilean transformation involves skewing the diagram.
answered yesterday
MovpasdMovpasd
513 bronze badges
New contributor
Movpasd is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered yesterday
MovpasdMovpasd
513 bronze badges
New contributor
Movpasd is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered yesterday
MovpasdMovpasd
513 bronze badges
answered yesterday
MovpasdMovpasd
513 bronze badges
513 bronze badges
New contributor
Movpasd is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Movpasd is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
$begingroup$
A Galilean transformation (or “Galilean boost”) is a change to a second inertial reference frame that is moving with constant velocity relative to the first one, but where the origin and axes align, so there is no translation at $t=0$ and no rotation at any time.
Imagine a bicyclist passing by you. His frame is boosted from yours. Yours is boosted from his, in the opposite direction.
Galilean boosts are the Newtonian equivalent of Lorentz boosts in Special Relativity.
In a translation, the frames do not have any relative motion. They just have different origins (but aligned axes).
answered yesterday
G. SmithG. Smith
22k1 gold badge40 silver badges74 bronze badges
$endgroup$
add a comment |
$begingroup$
A Galilean transformation (or “Galilean boost”) is a change to a second inertial reference frame that is moving with constant velocity relative to the first one, but where the origin and axes align, so there is no translation at $t=0$ and no rotation at any time.
Imagine a bicyclist passing by you. His frame is boosted from yours. Yours is boosted from his, in the opposite direction.
Galilean boosts are the Newtonian equivalent of Lorentz boosts in Special Relativity.
In a translation, the frames do not have any relative motion. They just have different origins (but aligned axes).
answered yesterday
G. SmithG. Smith
22k1 gold badge40 silver badges74 bronze badges
$endgroup$
add a comment |
$begingroup$
A Galilean transformation (or “Galilean boost”) is a change to a second inertial reference frame that is moving with constant velocity relative to the first one, but where the origin and axes align, so there is no translation at $t=0$ and no rotation at any time.
Imagine a bicyclist passing by you. His frame is boosted from yours. Yours is boosted from his, in the opposite direction.
Galilean boosts are the Newtonian equivalent of Lorentz boosts in Special Relativity.
In a translation, the frames do not have any relative motion. They just have different origins (but aligned axes).
answered yesterday
G. SmithG. Smith
22k1 gold badge40 silver badges74 bronze badges
$endgroup$
A Galilean transformation (or “Galilean boost”) is a change to a second inertial reference frame that is moving with constant velocity relative to the first one, but where the origin and axes align, so there is no translation at $t=0$ and no rotation at any time.
Imagine a bicyclist passing by you. His frame is boosted from yours. Yours is boosted from his, in the opposite direction.
Galilean boosts are the Newtonian equivalent of Lorentz boosts in Special Relativity.
In a translation, the frames do not have any relative motion. They just have different origins (but aligned axes).
answered yesterday
G. SmithG. Smith
22k1 gold badge40 silver badges74 bronze badges
edited 23 hours ago
answered yesterday
G. SmithG. Smith
22k1 gold badge40 silver badges74 bronze badges
answered yesterday
G. SmithG. Smith
22k1 gold badge40 silver badges74 bronze badges
answered yesterday
G. SmithG. Smith
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22k1 gold badge40 silver badges74 bronze badges
add a comment |
add a comment |
$begingroup$
A galilean boost changes your reference frame. A translation only changes your position in the same reference frame.
answered 22 hours ago
my2ctsmy2cts
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$endgroup$
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$begingroup$
A galilean boost changes your reference frame. A translation only changes your position in the same reference frame.
answered 22 hours ago
my2ctsmy2cts
7,8152 gold badges7 silver badges23 bronze badges
$endgroup$
add a comment |
$begingroup$
A galilean boost changes your reference frame. A translation only changes your position in the same reference frame.
answered 22 hours ago
my2ctsmy2cts
7,8152 gold badges7 silver badges23 bronze badges
$endgroup$
A galilean boost changes your reference frame. A translation only changes your position in the same reference frame.
answered 22 hours ago
my2ctsmy2cts
7,8152 gold badges7 silver badges23 bronze badges
answered 22 hours ago
my2ctsmy2cts
7,8152 gold badges7 silver badges23 bronze badges
answered 22 hours ago
my2ctsmy2cts
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answered 22 hours ago
my2ctsmy2cts
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