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3.1 Distinguish between the following approaches for solving problems. 3.1.1 The method of applying Newton's second law from the Lagrangean method. 3.1.2 The method of applying the Lagrangean from the Hamiltonian method. 3.2 A simple pendulum consists of a particle of mass m on an inextensible massless string of length {. The kinetic energy of the system in Cartesian coordinates is given by: T = m (x² + y²) where x and y may also be expressed in their polar coordinates format as x = { sin 0, and y = - cos 0 respectively.

3.1 Distinguish between the following approaches for solving problems. 3.1.1 The method of applying Newton's second law from the Lagrangean method. 3.1.2 The method of applying the Lagrangean from the Hamiltonian method. 3.2 A simple pendulum consists of a particle of mass m on an inextensible massless string of length {. The kinetic energy of the system in Cartesian coordinates is given by: T = m (x² + y²) where x and y may also be expressed in their polar coordinates format as x = { sin 0, and y = - cos 0 respectively.

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3.2.2 State the number of degrees of freedom and the number (name them also) of the generalised coordinates of the system? 3.2.3 From the Euler-Lagrange equation of motion: ƏL (OL) - = 0, dt dak да Show that the equation of motion for this system is given by: 0 + 20 = 0 3.2.4 What can you conclude about the system from this equation of motion?
Transcribed Image Text:3.2.2 State the number of degrees of freedom and the number (name them also) of the generalised coordinates of the system? 3.2.3 From the Euler-Lagrange equation of motion: ƏL (OL) - = 0, dt dak да Show that the equation of motion for this system is given by: 0 + 20 = 0 3.2.4 What can you conclude about the system from this equation of motion?
3.1 Distinguish between the following approaches for solving problems. 3.1.1 The method of applying Newton's second law from the Lagrangean method. 3.1.2 The method of applying the Lagrangean from the Hamiltonian method. 3.2 A simple pendulum consists of a particle of mass m on an inextensible massless string of length {. The kinetic energy of the system in Cartesian coordinates is given by: T = ²m (x² + y²) where x and y may also be expressed in their polar coordinates format as x = { sin 0, and y = - cos 0 respectively.
Transcribed Image Text:3.1 Distinguish between the following approaches for solving problems. 3.1.1 The method of applying Newton's second law from the Lagrangean method. 3.1.2 The method of applying the Lagrangean from the Hamiltonian method. 3.2 A simple pendulum consists of a particle of mass m on an inextensible massless string of length {. The kinetic energy of the system in Cartesian coordinates is given by: T = ²m (x² + y²) where x and y may also be expressed in their polar coordinates format as x = { sin 0, and y = - cos 0 respectively.
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