Tensorrechnung at Universität Stuttgart

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Exemplary flashcards for Tensorrechnung at the Universität Stuttgart on StudySmarter:

Wie sind die gausschen Zahlen definiert?

Exemplary flashcards for Tensorrechnung at the Universität Stuttgart on StudySmarter:

Was ist die Definition der Kinematik?

Exemplary flashcards for Tensorrechnung at the Universität Stuttgart on StudySmarter:

Was ist die Definition der Kinetik? Was ist in ihr enthalten?

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How is work defnied?

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Integration von 1/x ?

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Integration von -1/(x^2) ?

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Integration von e^x

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What is the mechanical quilibrium?

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What is the "Hill-Mandel macrohomogeneity condition" about? Advantages?

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What does "coarse mesh" mean in german?

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Explain Newton's second law

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What are  Euler-Lagragian Euqations?

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Exemplary flashcards for Tensorrechnung at the Universität Stuttgart on StudySmarter:

Tensorrechnung

Wie sind die gausschen Zahlen definiert?

Verallgemeinerung der ganzen Zahlen in den komplexen Zahlen


Eine gaußsche Zahl  g   ist durch

g = a + bi

gegeben, wobei   a   und b ganze Zahlen sind!

Tensorrechnung

Was ist die Definition der Kinematik?

Ein Gebiet der Mechanik, das die Bewegung von Körpern rein geometrisch beschreibt mit den Größen Zeit, Ort, Geschwindigkeit und Beschleunigung. Unberücksichtigt bleiben die Kraft, die Masse der Körper und alle davon abgeleiteten Größen wie Impuls oder Energie. Die Kinematik beschreibt somit nur, wie sich ein Körper bewegt, und wird daher auch als Bewegungslehre bezeichnet. Warum sich ein Körper bewegt, bleibt anderen Gebieten der Mechanik überlassen.

Tensorrechnung

Was ist die Definition der Kinetik? Was ist in ihr enthalten?

Die Kinetik beschreibt die Änderung der Bewegungsgrößen (Ort, Geschwindigkeit und Beschleunigung) unter Einwirkung von Kräften  und berücksichtigt dabei auch die Masse der bewegten Körper. 

Leitungssatz, Energiesatz, Arbeitssatz

Tensorrechnung

How is work defnied?

Work equals force times displacement:


W = F*u

Tensorrechnung

Integration von 1/x ?

ln(x)

Tensorrechnung

Integration von -1/(x^2) ?

1/x

Tensorrechnung

Integration von e^x

e^x

Tensorrechnung

What is the mechanical quilibrium?

Stable state, sum of the forces quals zero.

Tensorrechnung

What is the "Hill-Mandel macrohomogeneity condition" about? Advantages?

Voigt and Reuss way to average the microscopic properties isn't quite accurate. To be more accurate the Hill-Mandel condition transfers given macroscopic variables like prescribed deformationgradients to the microstructure via boundary conditions at the surface of the RVE.

Tensorrechnung

What does "coarse mesh" mean in german?

Grobes Netz

Tensorrechnung

Explain Newton's second law

The second law of motion describes what happens to the massive body when acted upon by an external force.  The law states that the force acting on the body is equal to the product of its mass and acceleration. 


When a constant force acts on a body, the forces results in the acceleration of the body.  However, if the object is already in motion, or if this situation is viewed from a moving frame of reference, the body might appear to speed up or slow down or change its direction depending on the direction of the force.

F=ma 

Tensorrechnung

What are  Euler-Lagragian Euqations?

In the calculus of variations, the Euler equation[1] is a second-order partial differential equation whose solutions are the functions for which a given functional is stationary. It was developed by Swiss mathematician Leonhard Euler and Italian mathematician Joseph-Louis Lagrange in the 1750s.

Because a differentiable functional is stationary at its local extrema, the Euler–Lagrange equation is useful for solving optimization problems in which, given some functional, one seeks the function minimizing or maximizing it. This is analogous to Fermat's theorem in calculus, stating that at any point where a differentiable function attains a local extremum its derivative is zero. 

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