The proof of mass vector.
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From: yen, ka-in on 25 Jun 2006 20:01 Any further questions? The proof of mass vector. Ka-In Yen http://www.geocities.com/redlorikee Introduction: In this paper, we will prove that linear mass density and surface mass density are vector, and the application of mass vector is presented. 1. The unit of vector. In physics, The unit of three-dimensional cartesian coordinate systems is meter. In this paper, a point of 3-D coordinate system is written as (p1,p2,p3) m, or (p:3) m and a vector is written as <a,b,c> m, or <a:3> m or l m<i,j,k> = <a,b,c> m where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector, and <i,j,k> is a unit vector which gives the direction of the vector. For three reasons, a magnitude of a vector can not add to a scalar: i) The magnitude belongs to the set of vector; it's a portion of a vector. Scalar belongs to a field. ii) The magnitude is real non-negative number, but scalar is real number. iii) The unit of magnitude is meter, but scalar has no unit. This is a major difference between physics and mathematics. 5m+3 is meaningless. 2. Linear mass density is a vector. The mass of a string is M kg, and the length of the string is l m<i:3>. Where l m is the magnitude of the length, and <i:3> is a 3-D unit vector which gives the direction of the string. Then the linear mass density of the string is: M/(l<i:3>)=(M/l) (kg/m)<i:3> The direction, <i:3>, is not changed by "division", so we can move <i:3> from denominator to numerator. A direction is changed by -1 only. A proof is found in Clifford algebras: [Proof] k/<a,b,c>=[k<a,b,c>]/[<a,b,c>^2] =(k/l) <i,j,k> where l is the magnitude of <a,b,c>, and <i,j,k> is the unit vector of <a,b,c>. [Proof] 3. Surface mass density is a vector. A parallelogram has two vectors: l m<i:3> and h m<j:3>. <i:3> and <j:3> are unit vectors. The area vector of the parallelogram is the cross product of these two vectors. l m<i:3> X h m<j:3>= lh (m^2 )<i:3>X<j:3> = lh abs(sin(theta)) (m^2)<k:3> Where theta is the angle between <i:3> and <j:3>. <k:3> is a unit vector which is perpendicular to <i:3> and <j:3>. For AXB=-BXA, an area has two directions. We can divide the area vector by the length vector. lh*abs(sin(theta))<k:3>/[l<i:3>] =h<i:3>X<j:3>/<i:3> =h(<i:3>X<j:3>)X<i:3> (The direction, <i:3>, is not changed by "division", and the division is replaced by a cross product.) =-h<i:3>X(<i:3>X<j:3>) =-h[<i:3>(<i:3>o<j:3>)-<j:3>(<i:3>o<i:3>)] (where o is dot product.) =-h(cos(theta)<i:3>-<j:3>) =h(<j:3>-cos(theta)<i:3>) m The result is a rectangle, not the original parallelogram. We can test the result. h(<j:3>-cos(theta)<i:3>)Xl<i:3>=lh m^2<j:3>X<i:3> The magnitude of the area vector is conserved, but the direction is opposite. The mass of a round plate is M kg, and the area vector is A m^2<i:3>; then the surface mass density is M kg/(A m^2<i:3>)=M/A (kg/m^2)<i:3> 4. Mass vector in physics. Mass vector has been found in two equations: 1) the velocity equation of string. 2) Bernoulli's equation. i) For waves on a string, we have the velocity equation: v=sqrt(tau/mu). v is velocity of wave, tau is tension applying to string, and mu is linear mass density of string. We can rewrite the equation: mu=tau/v^2. In the above equation, the mu is parallel to tau, and both of them are vector. ii) Bernoulli's equation is: P + k*v^2/2=C (P is pressure, k is volume density, and v is velocity. Here we neglect the gravitational term.) Multiplying cross area vector A m^2<i:3> of a string to Bernoulli's equation(where <i:3> is a unit vector), P*A<i:3> + k*A<i:3>*v^2/2=C*A<i:3> F<i:3> + L<i:3>*v^2/2=C*A<i:3> (where F is the magnitude of force, and L is the magnitude of linear mass density.) These two equations are well used in the theory "Magnetic force: Combining Drag force and Bernoulli force of ether dynamics." For detail, please refer to my site: http://www.geocities.com/redlorikee
From: Eric Gisse on 29 Jun 2006 21:58 Ka-In Yen wrote: [...] > > For your reference: vector division in Matlab. > > http://newsreader.mathworks.com/WebX?14(a)88.ug0LaenUYOM.0@.ef097af Worthless. Using the method MATLAB uses, there are an infinite number of matricies that a and b that create the product a/b. You repost the same tripe about once a month in the same thread over and over while ignoring criticisms that would cause you to have to abandon your work.
From: Ka-In Yen on 30 Jun 2006 20:31 Eric Gisse wrote: > Ka-In Yen wrote: > > [...] > > > > > For your reference: vector division in Matlab. > > > > http://newsreader.mathworks.com/WebX?14(a)88.ug0LaenUYOM.0@.ef097af > > Worthless. Using the method MATLAB uses, there are an infinite number > of matricies that a and b that create the product a/b. Obviously you did not read Titus's posting carefully. Please try again: http://www.google.com/search?hl=en&lr=&q=%22vector+division+in+matlab%22 > You repost the same tripe about once a month in the same thread over > and over while ignoring criticisms that would cause you to have to > abandon your work. Home work for Eric Gisse: A rectangle sits in 3D space. The area vector of the rectangle is A, and the legth vector of one side of the rectangle is L. Please find the length vector of the other side of the rectangle?
From: Phineas T Puddleduck on 30 Jun 2006 20:32 In article <1151713860.481999.282010(a)p79g2000cwp.googlegroups.com>, Ka-In Yen <yenkain(a)yahoo.com.tw> wrote: > Eric Gisse wrote: > > Ka-In Yen wrote: > > > > [...] > > > > > > > > For your reference: vector division in Matlab. > > > > > > http://newsreader.mathworks.com/WebX?14(a)88.ug0LaenUYOM.0@.ef097af > > > > Worthless. Using the method MATLAB uses, there are an infinite number > > of matricies that a and b that create the product a/b. > > Obviously you did not read Titus's posting carefully. Please try again: > > http://www.google.com/search?hl=en&lr=&q=%22vector+division+in+matlab%22 > > > > > You repost the same tripe about once a month in the same thread over > > and over while ignoring criticisms that would cause you to have to > > abandon your work. > > Home work for Eric Gisse: > A rectangle sits in 3D space. The area vector of the rectangle is A, > and the legth vector of one side of the rectangle is L. Please find > the length vector of the other side of the rectangle? > Are you truly this clueless? -- The greatest enemy of science is pseudoscience. e=pc and p=hk Jaffa cakes. Sweet delicious orangey jaffa goodness, and an abject lesson why parroting information from the web will not teach you cosmology. Official emperor of sci.physics, head mumbler of the "Cult of INSANE SCIENCE". Please pay no attention to my butt poking forward, it is expanding. Relf's Law? "Bullshit repeated to the limit of infinity asymptotically approaches the odour of roses." -- Posted via a free Usenet account from http://www.teranews.com
From: Eric Gisse on 30 Jun 2006 21:36
Ka-In Yen wrote: > Eric Gisse wrote: > > Ka-In Yen wrote: > > > > [...] > > > > > > > > For your reference: vector division in Matlab. > > > > > > http://newsreader.mathworks.com/WebX?14(a)88.ug0LaenUYOM.0@.ef097af > > > > Worthless. Using the method MATLAB uses, there are an infinite number > > of matricies that a and b that create the product a/b. > > Obviously you did not read Titus's posting carefully. Please try again: > > http://www.google.com/search?hl=en&lr=&q=%22vector+division+in+matlab%22 What part of "underdetermined" confuses you? Vector division is not defined at all, much less that way, because there is no unique inverse! > > > > > You repost the same tripe about once a month in the same thread over > > and over while ignoring criticisms that would cause you to have to > > abandon your work. > > Home work for Eric Gisse: > A rectangle sits in 3D space. The area vector of the rectangle is A, > and the legth vector of one side of the rectangle is L. Please find > the length vector of the other side of the rectangle? LENGTH IS NOT A VECTOR. AREA IS NOT A VECTOR. |