Forest UCM MiNF - Revision history

Foretony: /* Magnitude of the Tides */

2021-12-06T02:15:59Z

Magnitude of the Tides

2021-12-06T02:14:52Z

Magnitude of the Tides

2021-12-06T01:59:39Z

The tides view by a ref frame accelerating towards the moon

2021-12-06T01:46:54Z

The tides view by a ref frame accelerating towards the moon

2021-12-06T01:46:23Z

The tides view by a ref frame accelerating towards the moon

2021-12-06T01:02:39Z

The tides view by a ref frame accelerating towards the moon

2021-12-06T01:01:47Z

The tides view by a ref frame accelerating towards the moon

2021-11-15T05:25:55Z

The tides view by a ref frame accelerating towards the moon

2021-11-15T05:21:21Z

Pedulum in an accelerating car

2021-11-15T05:20:34Z

Pedulum in an accelerating car

@@ Line 170: / Line 170: @@
-:<math> U_{\mbox{tide-2}}  = - \int \vec F_o \cdot d \hat x= \int G \frac{M_m M_o }{d_0^2}\hat {d}_0 \cdot d \hat x</math>
+:-<math> U_{\mbox{tide-2}}  = -(- \int \vec F_o \cdot d \hat x)= \int G \frac{M_m M_o }{d_0^2}\hat {d}_0 \cdot d \hat x</math>
 ::<math> =  G \frac{M_m M_o}{d_0^2}\int\hat {d}_0 \cdot d \hat x</math>  Since <math>d_0</math> is at fixed distance
 ::<math> =  G \frac{M_mM_o }{d_0^2}\int\ d x</math>  Since <math>d_0</math> is parallel to x

@@ Line 161: / Line 161: @@
-:<math>\vec{F}_{\mbox{tide}} =  G \frac{M_m M_o}{d^3}\vec d  -  G \frac{M_m }{d_0^3}\vec d_0 \equiv - \nabla U_{\mbox{tide-1}}- \nabla U_{\mbox{tide-2}}</math>
+:<math>\vec{F}_{\mbox{tide}} =  G \frac{M_m M_o}{d^3}\vec d  -  G \frac{M_m }{d_0^3}\vec d_0 \equiv - \nabla U_{\mbox{tide-1}}- (-\nabla U_{\mbox{tide-2}})</math>
 :<math>G \frac{M_m M_o}{d^3}\vec d \equiv - \nabla U_{\mbox{tide-1}}</math>
@@ Line 167: / Line 167: @@
-:<math> G \frac{M_m M_o}{d_0^3}\vec d_0 \equiv  \nabla U_{\mbox{tide-2}}</math>
+:<math> G \frac{M_m M_o}{d_0^3}\vec d_0 \equiv - \nabla U_{\mbox{tide-2}}</math>

@@ Line 119: / Line 119: @@
 where
-:<math>\vec F_N =</math> a net non-graviational force hold the mass M_o in top of the ocean (Bouyant force)= M(displaced water)*g
+:<math>\vec F_N =</math> a net non-graviational force hold the mass M_o in top of the ocean (Bouyant force)= M(displaced water)*g = constant force independent of position
 :<math> M_o \ddot \vec r =  \left ( M_o \vec g + {\vec F}_N +  G \frac{M_m M_o}{d^3} \vec d \right ) -  G \frac{M_m }{d_0^3}\vec d_0  </math>

@@ Line 119: / Line 119: @@
 where
-:<math>\vec F_N =</math> a net non-graviational force hold the mass M_o in top of the ocean (Bouyant force)= M(dis0laced water)*g
+:<math>\vec F_N =</math> a net non-graviational force hold the mass M_o in top of the ocean (Bouyant force)= M(displaced water)*g
 :<math> M_o \ddot \vec r =  \left ( M_o \vec g + {\vec F}_N +  G \frac{M_m M_o}{d^3} \vec d \right ) -  G \frac{M_m }{d_0^3}\vec d_0  </math>

@@ Line 119: / Line 119: @@
 where
-:<math>\vec F_N =</math> a net non-graviational force hold the mass M_o in top of the ocean (Bouyant force)
+:<math>\vec F_N =</math> a net non-graviational force hold the mass M_o in top of the ocean (Bouyant force)= M(dis0laced water)*g
 :<math> M_o \ddot \vec r =  \left ( M_o \vec g + {\vec F}_N +  G \frac{M_m M_o}{d^3} \vec d \right ) -  G \frac{M_m }{d_0^3}\vec d_0  </math>

@@ Line 121: / Line 121: @@
 :<math>\vec F_N =</math> a net non-graviational force hold the mass M_o in top of the ocean (Bouyant force)
-:<math> M_o \ddot \vec r =  \left ( M_o \vec g + \vec F_N +  G \frac{M_m M_o}{d^3} \vec d \right ) -  G \frac{M_m }{d_0^3}\vec d_0  </math>
+:<math> M_o \ddot \vec r =  \left ( M_o \vec g + {\vec F}_N +  G \frac{M_m M_o}{d^3} \vec d \right ) -  G \frac{M_m }{d_0^3}\vec d_0  </math>
 :: <math>= M_o \vec g + \vec F_N + \vec{F}_{\mbox{tide}}</math>

@@ Line 114: / Line 114: @@
 As seen in the Earth non-inertial reference frame
-:<math>M_o \ddot \vec r = \sum \vec F - M_o \vec A</math>
+:<math>M_o \ddot {\vec r} = \sum \vec F - M_o \vec A</math>
 :: <math>= \left ( M_o \vec g + \vec F_N +  G \frac{M_m M_o}{d^3}\vec d \right ) -  G \frac{M_m }{d_0^3}\vec d_0 </math>

@@ Line 77: / Line 77: @@
 :<math>\vec{r} = (l \sin \theta + \frac{1}{2} a t^2) \hat i +  l \cos \theta \hat j</math>
-:<math>\dot \vec{r} = (l \cos \theta \dot \theta +  a t ) \hat i +  \sin \theta \dot \theta \hat j</math>
+:<math>\dot {\vec{r}} = (l \cos \theta \dot {\theta} +  a t ) \hat i +  \sin \theta \dot {\theta} \hat j</math>
 :<math> T = \frac{1}{2} mv^2 = \frac{1}{2} m \left ( (l \cos \theta \dot \theta +  a t)^2 + \sin^2 \theta \dot \theta^2 \right )</math>