Reductions of Topologically Massive Gravity I: Hamiltonian Analysis of The Second Order Degenerate Lagrangians

We study the Hamiltonian formalisms of the second order degenerate Cl`ement and Sar{\i}o\u{g}lu-Tekin Lagrangians. The Dirac-Bergmann constraint algorithm is employed while arriving at the total Hamiltonian functions and the Hamilton’s equations on the associated momemtum phase spaces whereas the Gotay-Nester-Hinds algorithm is run while investigating the Skinner-Rusk unified formalism on the proper Whitney bundles.