Escalares, Vectores y Tensores Cartesianos

Escalares, Vectores y Tensores Cartesianos

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Algebra Tensorial

Resumen

1. Suma de vectores        simbólica: [pic 45]  , índice: [pic 46] 
2. Multiplicación

1. Vector por escalar [pic 47] 
2. Producto punto entre dos vectores [pic 48] , [pic 49] [pic 50] ángulo entre los vectores [pic 51] .

[pic 52]

1. Producto cruz o producto vectorial  [pic 53] , [pic 54] [pic 55] ángulo entre los vectores [pic 56] , [pic 57] vector ortogonal a [pic 58].

[pic 59]

1. Triple producto escalar [pic 60]

[pic 61]

1. Triple producto cruz  [pic 62] Identidad [pic 63] : [pic 64] ,  [pic 65] ;          [pic 66]

[pic 67] 

Recordando:         [pic 68] ,        [pic 69] ,        [pic 70] 

1. Producto tensorial de dos vectores (diada) [pic 71] 

Expandiendo [pic 72]        Forma nonión de la diada[pic 73]

Notación alternativa [pic 74] 

Diádica[pic 75] Suma de diadas         [pic 76] 

1. Producto vector-diada

1. [pic 77] 
2. [pic 78] 
3. [pic 79] 
4. [pic 80] 

1. Producto diada-diada [pic 81] 
2. Producto vector-tensor

1. [pic 82] 
2. [pic 83] 

[pic 84]

1. Producto tensor – tensor [pic 85] 

Ejemplo: Doble producto de diadas

1. [pic 86] 
2. [pic 87] 

Notación índice

[pic 88] escalar (tensor de orden cero) [pic 89] 

[pic 90] vector (tensor de primer orden) [pic 91] [pic 92] sus tres componentes

[pic 93] diada (tensor de segundo orden) [pic 94] [pic 95] sus nueve componentes