The How Energy from Chaos becomes ,The Spin of monads ,Their Energy – Stores , And Photons - Giorgallides, Marcos (IJRDO - Journal of Mechanical And Civil Engineering, 2018)
From Mechanics in case that , in an Axisymmetric Rotating Body , with constant Angular-Velocity , w , the moment of Inertia , span style="font-family: Cambria Math;font-size:8pt;color:rgb(0,0,0);font-style:normal;font-variant:normal;"> = span style="font-family: Cambria Math;font-size:8pt;color:rgb(0,0,0);font-style:normal;font-variant:normal;"> , is equal about the two ofthe three Principal axis , then , 1.. The Angular – velocity - vector , , describes the Ellipsoid of Angular Velocity and its nib describes a Cone of which Plane-Base is Fixed , and Simultaneously , 2.. The Angular-Momentum , , describes the Ellipsoid of Angular-Momentum and its nib describes a Cone also of which Plane-Base is also Fixed . 3.. The Nib of Angular – velocity - vector , , describes on the Tangential-Plane of the Angular-Momentum-Ellipsoid , the Herpolhode , while , 4.. The Nib of Angular-Momentum , , describes on the Tangential-Plane , of the Angular-Velocity-Ellipsoid , the Polhode . 5.. The Fixed-Tangential-Planes on , , and , , nib are alternately Perpendicular to , B̅ , and , w̅ , central axes of rotation . 6.. The Kinetic Rotational – Energy ofmonad , which is the Work in monad , is the Scalar quantity , L , The Vector Angular Momentum quantity is , , and the Vector Angular - Velocity quantity is , , which Three monads are related as . = 2L = J . w² where J = The moment of inertia around the axis of rotation. All above happen in , Material-Point , where the Positive ⊕ constituent , is Eternally selfrolling on the Negative ⊝ constituent , with Angular-Velocity , w , in Infinite Spherical traces , either at Great-circles [+or -] , or Small-circles , [+] where is the Clockwise Left direction , and [ - ] where is the Anti-Clockwise Right direction , or any other close Spherical-curve , and by Applying all laws of Mechanics into this Energy - Chaos , is thus created the → First–Discrete – Energy–monad , the Material Point i.e. , The Quantum ofPhysics and , ofall Energy-Space-Universe . Article [65] is the completion ofprior [64M]. The Energy E dissipated per cycle is equal to the Work Wd → E = h.f = h(1+ √5 ] ) 4π . [ br>span style="font-family: ;font-size:12pt;color:rgb(0,0,0);font-style:normal;font-variant:normal;"> ] = 8.kζ(πr²) , and Stored in monad , which is a Stationary Wave , in ,n, loops as , span style="font-family: Cambria Math;font-size:8pt;color:rgb(0,0,0);font-style:normal;font-variant:normal;"> = [ br>].span style="font-family: Cambria Math;font-size:8pt;color:rgb(0,0,0);font-style:normal;font-variant:normal;"> = [ br>]. n (√ br> The How Energy from Chaos Becomes Discrete - Monads and Spin Geometry has the Monad , the discrete continuity AB length becoming from the Zero-Point ≡ 0 , and Mechanics - Physics the Recent-Acquisition of the Material - Geometry , where Zero-point 0 =  = ⊕+⊝ = The Material-point = The Quantum = Positive Space and Negative Anti-Space . [58] Monad in Geometry → Linearly is , through mould of Parallel Theorem [44-45] ,which are the equal distances between points of parallel and line → In Plane is through mould of Squaring the circle [46-47] , where the two equal and perpendicular monads consist a Plane acquiring the common Plane- meter ,π, → In Space (volume) is through mould of the Duplication of the Cube [44-46] , where any two Unequal perpendicular monads acquire the common Space-meter ,³√2 , to be twice each other . Monad in Mechanics and Physics is → The Material-point = the discrete continuity |⊕+⊝ | = The Quantum through mould of Space –Anti-space in itself , which is the material dipole in inner monad Structure and is Identical with the Electromagnetic cycloidal field of Energy monads . This is , the Energy distance , the deep concept of Material-geometry . Energy monads presuppose Energy-Space Base (the caves beyond Planck`s length ,Gravity`s and Spaces levels ) the [PNS] Space Anti-Space as work → W = ∫ P.ds = 0 , which is the cause of Spaces existence and the motion of particles . Since are also Quantized then , this property is encountered in Stationary waves where energy , E , is proportional to angular velocity w . This property of particles , Angular momentum = The Spin , becomes from the Intrinsic , Inward , cycloidal wave motion, which is their cause of external motion as outward waves .[43] The varying lever arms , on cycloid-evolute is the cause of vibrations and which cause the EM-waves and Spin . Common-circle of radius , rc , is the common source of vibration excitation for the Space , Anti – space , considered as rotating with angular velocity ,w, and then their relative motion becomes the , Rolling of Space , ABC , on Anti-space AEBECE and since also this relative motion is applied on STPL [Six Triple Points Line] Mechanism , then DA , PA , points on it are the corresponding linear links of vibrations and Poles of rotation . [STPL] is a Geometrical Mechanism that produces and composite all opposite Space and Anti - space Points to Material-points → Waves ← the three Breakages [s² = ± (w̅.r)² , [i] = 2(wr)²] of [MFMF] mechanism under v̅ = c̅ thrust , and through it are becoming , The Fermions → [ ±.s²] and The Bosons → [v̅.i = [v̅.2(w̅.r)²] = [.2s² ] , [35] It was shown [33-36] that Un-clashed Fragments through center , O , consist the Medium-Field Material-Fragment → [ ± s² ] = [MFMF] = The Chaos , as base for all motions , and Gravity as force [i] , while the clashed with the constant velocity ,c̅, consist the Dark matter [ ±.c̅.s ] and the Dark energy [c̅.i] , declaring that → Antimatter-Galaxies and Antimatter – Asteroids can exist only as Dark-matter or and Dark-Energy and Not as Antimatter light , - c , alone , or from → Breakages [ ± s² = ± (wr)²] and [ i = 2(wr)² ] , where then become Waves Distance ds = |AAE| is the Work embedded in monads and it is what is vibrated with the Vibrating equations of motion , become , A → Particles , with Inherent Vibration , B → Gravity-Field-Energy , without Vibration C → Dark-matter-Energy constituents and as below , A.. [ ±v̅.s²] → Fermions and → [v̅.i] → Bosons , B.. [ ± s²] → [MFMF] Field ≡ The Energy - Chaos , and the binder Field is [ i ] → Gravity force , C.. [ ±c̅.s² ] → Dark matter , and the binder Gravity force [i] , [c̅.i] → The Expanding Dark energy, which both are moving with light velocity , c , causing the universe to grow. From above in , A , and , C, case → Energy as velocity , v̅, exists in the Discrete monads ,± v̅.s² and ± c̅.s².